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What is the general formula for any complex number?
in Mathematics by Bronze Status (8,688 points) | 16 views

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A complex number is part of the set of complex numbers which we represent as the symbol, $\mathbb{C}$. Thus any complex number is part of this set $\mathbb{C}$. Suppose we have complex number, $z$.

Now since its a complex number we can say that, $z$ is part of the set of complex numbers, $\mathbb{C}$, which we write as $z \in \mathbb{C}$
Now the general formula for our complex number, or any complex number, can be written as:
$z=a+b i$
where
$a$ and $b$ are real numbers i.e. $a$ and $b$ in the set of real numbers, $\mathbb{R}$, which we can again write as $a, b \in \mathbb{R}$

The complex number is made up of two parts. They are:

  • The real part, which is $a$ (We can show this as $\operatorname{Re}(z)=a$ )
  • The imaginary part, the number in front of the $i$, which is $b$ (We can show this as $\operatorname{Im}(z)=b$ )

(because its like how we show real numbers on the Cartesian plane $(x, y))$

by Bronze Status (8,688 points)

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