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How do I multiply complex numbers?
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Unlike, addition or subtraction, multiplying imaginary numbers isn't as straightforward although we still use the same idea of FOIL to multiply the two numbers (treat them like expressions). What usually happens is that we times an imaginary part by another imaginary part which results in a negative. Remember: $i^{2}=-1$

$z_{1} \times z_{2}=(a+b i) \times(x+y i)=a(x+y i)+b i(x+y i)$
$=a x+a y i+b x+b y i^{2}=a x+a y i+b x i-b y$
$=(a x-b y)+(a y+b x) i$
We can show the multiplication of $z_{1} \times z_{2}$ as $z_{1} z_{2}$
Remember to be careful when squaring $i$.
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