How do you multiply $(3+3i)(6-6i)$ in trigonometric form?

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Answer 1 · 2016-02-28T11:07:08

$(3 + 3i) * (6 - 6i) = 36$

$3 + 3i = 3sqrt2 e^{i(pi/4)}$

$6 - 6i = 6sqrt2 e^{i(-pi/4)}$

So,

$(3 + 3i) * (6 - 6i) = (3sqrt2 e^{i(pi/4)}) * (6sqrt2 e^{i(-pi/4)})$

$= (3sqrt2)(6sqrt2) * e^{i[(pi/4)+(-pi/4)]}$

$= 36 * e^{i(0)}$

$= 36$

How do you multiply (3+3i)(6-6i) (3+3i)(6-6i) in trigonometric form?