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Question Number 167119 by mathlove last updated on 07/Mar/22

$${(z+3i)}^{20}=?$$

Answered by mr W last updated on 07/Mar/22

$$z=a+bi$$$${(z+3i)}^{20}$$$$={(a+(b+3)i)}^{20}$$$$={(a^2+{(b+3)}^2)}^{10}{e}^{i\left(20{\tan }^{-1}\frac{b+3}{a}\right)}$$

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