Sum, Difference and Product of Complex Numbers

If $c_1 = a +ib$ and $c_2 = a' +ib'$ then the sum of $c_1$ and $c_2$ is

$$c_1 + c_2 = ( a+ a') + i( b + b')$$

and their difference is

$$c_1 - c_2 = ( a- a') + i( b - b')$$

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The product of $c_1$ and $c_2$ is

$$c_1 c_2 = (a +ib ) (a' +ib') = (aa' -bb')+ i( ab' + a'b)$$