Recent questions tagged complex

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Simplify the complex expression \[ (2-3 i)(-2+i) \]

asked Aug 3 in Mathematics by MathsGee Platinum (98.5k points) | 22 views

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Simplify the complex number \(5(3-2 i)+2 i(4+6 i)\)

asked Aug 3 in Mathematics by MathsGee Platinum (98.5k points) | 25 views

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Which expression is equivalent to \(9 x^2-16 y^2 ?\)

asked Jul 16 in Mathematics by Edzai Zvobwo Bronze Status (5.6k points) | 64 views

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(Lael and Nourouzi 2008) Let \((V, \mu, \nu)\) be an \(I F\)-normed space. Assume further that \(\mu(x, t)>0\) for all \(t>0\) implies \(x=0\).

asked May 21 in Mathematics by MathsGee Platinum (98.5k points) | 76 views

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Give an example of how to find the roots of a complex number.

asked Mar 29 in Mathematics by MathsGee Platinum (98.5k points) | 162 views

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What is a complex root?

asked Mar 29 in Mathematics by MathsGee Platinum (98.5k points) | 167 views

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What are the basic operations of complex numbers?

asked Mar 29 in Mathematics by MathsGee Platinum (98.5k points) | 202 views

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Explain the polar form of complex numbers with an example and use latex

asked Mar 29 in Mathematics by MathsGee Platinum (98.5k points) | 206 views

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What happens when you multiply a complex number by its conjugate?

asked Mar 29 in Mathematics by MathsGee Platinum (98.5k points) | 174 views

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Give 10 examples of complex conjugate pairs.

asked Mar 29 in Mathematics by MathsGee Platinum (98.5k points) | 198 views

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What is conjugation in complex numbers?

asked Mar 29 in Mathematics by MathsGee Platinum (98.5k points) | 186 views

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WHat are complex numbers?

asked Mar 29 in Mathematics by MathsGee Platinum (98.5k points) | 179 views

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The inverse of \(-i\) in the multiplicative group, \(1,-1, i,-i\) is

asked Mar 15 in Mathematics by MathsGee Platinum (98.5k points) | 567 views

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What is a zero-matrix?

asked Mar 7 in Mathematics by Maths Genie Bronze Status (8.8k points) | 249 views

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Multiply \(3+\mathrm{i} \sqrt{3}\) by its complex conjugate.

asked Feb 20 in Mathematics by Maths Genie Bronze Status (8.8k points) | 205 views

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For \(\mathrm{i}=\sqrt{-1}\), what is the result of subtracting \((2+4 \mathrm{i})\) from \((-5+6 \mathrm{i}) ?\)

asked Feb 20 in Mathematics by Maths Genie Bronze Status (8.8k points) | 134 views

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What is a CCP Complex?

asked Feb 13 in General Knowledge by Maths Genie Bronze Status (8.8k points) | 176 views

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What is a complex number?

asked Jan 27 in Mathematics by AstraNova Diamond (55.6k points) | 183 views

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What is the formula for the area of a parallelogram?

asked Jan 27 in Mathematics by AstraNova Diamond (55.6k points) | 152 views

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Prove that the roots of a polynomial with real coefficients are either real or come in conjugate pairs.

asked Jan 27 in Mathematics by AstraNova Diamond (55.6k points) | 148 views

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If \(x\) is a real number such that \((x-3)(x-1)(x+1)(x+3)+16=116^2\), what is the largest possible value of \(x\) ?

asked Dec 8, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 172 views

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How many quadratics are there with these properties?

asked Dec 8, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 182 views

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How many cool sequences are there?

asked Dec 8, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 115 views

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Let \(H\) be a regular hexagon with area 360 . Three distinct vertices \(X, Y\), and \(Z\) are picked randomly, with all possible triples of distinct vertices equally likely. Let \(A, B\), and \(C\) be the unpicked vertices.

asked Dec 8, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 130 views

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The roots of the polynomial \(x^4-4 i x^3+3 x^2-14 i x-44\) form the vertices of a parallelogram in the complex plane. What is the area of the parallelogram?

asked Dec 8, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 117 views

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The imaginary part of \((3+2 \sqrt{-54})^{\frac{1}{2}}-(3-2 \sqrt{-54})^{\frac{1}{2}}\) can be

asked Nov 29, 2022 in Mathematics by Maths Genie Bronze Status (8.8k points) | 114 views

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We have a chessboard of size \(\left(k^2-k+1\right) \times\left(k^2-k+1\right)\), where \(k-1=p\) is a prime number.

asked Sep 23, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 257 views

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The positive integers \(a, b, c, d, p\), and \(q\) satisfy \(a d-b c=1\) and \(\frac{a}{b}>\frac{p}{q}>\frac{c}{d}\). Prove that:

asked Sep 23, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 129 views

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Let \(x \leq y \leq z\) be real numbers such that \(x y+y z+z x=1\). Prove that \(x z<\frac{1}{2}\). Is it possible to improve the value of constant \(\frac{1}{2}\) ?

asked Sep 23, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 233 views

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asked Sep 23, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 181 views

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If \(a, b, c\) are nonnegative real numbers with \(a^2+b^2+c^2=1\), prove that

asked Sep 23, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 137 views

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For any set \(A\) of positive integers, let \(n_A\) be the number of triples \((x, y, z)\) of elements of \(A\) with \(x<y\) and \(x+y=z\). If \(A\) is a seven-element set, find the maximum possible value of \(n_A\).

asked Sep 22, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 148 views

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Messages are coded as sequences of zeros and ones. Only sequences with not more than two consecutive zeros or ones are allowed. How many permitted 12digit sequences are there?

asked Sep 22, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 185 views

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Let \(T(n)\) be the sum of the decimal digits of a natural number \(n\).

asked Sep 22, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 142 views

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Let \(s(t)\) denote the number of digits of a natural number \(t\). Find all solutions to the system

asked Sep 22, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 129 views

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Let \(a, b\) and \(c\) be positive real numbers. Prove that \[ \frac{a}{b}+\frac{b}{c}+\frac{c}{a} \leq \frac{a^2}{b^2}+\frac{b^2}{c^2}+\frac{c^2}{a^2} . \]

asked Sep 22, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 110 views

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If \(a, b, c\) are positive real numbers that satisfy \[ \frac{a^2}{1+a^2}+\frac{b^2}{1+b^2}+\frac{c^2}{1+c^2}=1 \] prove that \(|a b c| \leq \frac{1}{2 \sqrt{2}}\)

asked Sep 22, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 125 views

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If \(a, b, c\) are positive real numbers that satisfy \(a^2+b^2+c^2=1\), find the minimal value of

asked Sep 22, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 112 views

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Given that \(z=3-3 \mathrm{i}\) express, in the form \(a+\mathrm{i} b\), where \(a\) and \(b\) are real numbers,

asked Sep 13, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 108 views

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Find \(\frac{\mathrm{z}_2}{\mathrm{z}_1}\) in the form \(a+\mathrm{i} b\), where \(a\) and \(b\) are expressed in terms of \(p\).

asked Sep 13, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 145 views

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Find the roots of the equation \[ z^2+2 z+17=0, \]

asked Sep 13, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 163 views

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\[ z=\sqrt{3}-\mathrm{i} . \] \(\mathrm{z}^*\) is the complex conjugate of \(\mathrm{z}\). (a) Show that \(\frac{z}{z^*}=\frac{1}{2}-\frac{\sqrt{3}}{2} i\).

asked Sep 13, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 160 views

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The complex number \(z\) is defined by

asked Sep 13, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 126 views

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The complex numbers \(z_1\) and \(z_2\) are given by \[ z_1=2-\mathrm{i} \text { and } z_2=-8+9 \mathrm{i} \]

asked Sep 13, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 136 views

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The complex numbers \(z_1\) and \(z_2\) are given by \[ z_1=2+8 \mathrm{i} \text { and } z_2=1-\mathrm{i} \]

asked Sep 13, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 239 views

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\[ f(x)=x^3+x^2+44 x+150 \] Given that \(\mathrm{f}(x)=(x+3)\left(x^2+a x+b\right)\), where \(a\) and \(b\) are real constants,

asked Sep 13, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 115 views

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\[ z=2-3 \mathrm{i} \] (a) Show that \(z^2=-5-12 \mathrm{i}\).

asked Sep 13, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 122 views

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Given that \(1-2 \mathrm{i}\) is a complex solution of \(\mathrm{f}(x)=0\),

asked Sep 13, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 104 views

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Given that \(z=-3+4 \mathrm{i}\), find the modulus of \(z\),

asked Sep 13, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 144 views

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What are non-real numbers in mathematics?

asked Sep 7, 2022 in Mathematics by MathsGee Platinum (98.5k points) | 214 views

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