How do you write the complex number in trigonometric form $-7i$ ?

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Answer 1 · 2018-01-06T10:22:39

The answer is $=7(cos(-pi/2)+isin(-pi/2))=7e^(-1/2ipi)$

Any complex number $z=a+ib$ can be represented as

$z=r(costheta+isintheta)$

Where,

$r=||z||=sqrt(a^2+b^2)$

$costheta=a/(||z||)$

and

$sintheta=b/||z||$

Here, we have

$z=0-7i$

$||z||=sqrt((0)^2+(-7)^2)=7$

$z=7((0/7)+(-7/7)i)$

$costheta=0$ and $sin theta=-1$

Therefore,

$theta =-pi/2$ , $[mod 2pi]$

So,

$z=7(cos(-pi/2)+isin(-pi/2))$

How do you write the complex number in trigonometric form -7i-7i?