Mathematics: Express the complex number in trigonometric form. -4i

Express the complex number in trigonometric form.

PencilLover101

18.01.2022

-4i = 4(cos 270 +i sin 270)

Step-by-step explanation:

We have a+ib = r(cosθ+isinθ)

$r=\sqrt{a^2+b^2}\texttt{ and }tan\theta =\frac{b}{a}$

Here a = 0 and b = -4

Substituting

$r=\sqrt{0^2+(-4)^2}\\\\r=4\\\\tan\theta =\frac{-4}{0}\\\\\theta =270^0\texttt{(Since a is zero and b is negative)}$

-4i = 4(cos 270 +i sin 270)

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gl648809

16.04.2022

Excuse me, you have to put the rest of the question on here so that we can give you a good answer.

-Miri

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