How do you write the complex number in trigonometric form $- 5 i$ $-5i$ ?

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Answer 1 · 2017-02-26T08:10:55

The answer is $= 5 (cos (- \frac{1}{2} π) + i sin (- \frac{1}{2} π))$ $=5(cos(-1/2pi)+isin (-1/2pi))$

The trigonometric form of a complex number is

$z = r (cos θ + i sin θ)$ $z=r(costheta+isin theta)$

Here, we have

$z = - 5 i$ $z=-5i$

Therefore,

$r = 5$ $r=5$

$cos θ = 0$ $costheta=0$

$sin θ = - 1$ $sin theta=-1$

So, $θ = - \frac{1}{2} π$ $theta=-1/2pi$

$z = 5 (cos (- \frac{1}{2} π) + i sin (- \frac{1}{2} π))$ $z=5(cos(-1/2pi)+isin (-1/2pi))$

$= 5 e^{- \frac{1}{2} i π}$ $=5e^(-1/2ipi)$

How do you write the complex number in trigonometric form −5i-5i?