How do I find the trigonometric form of the complex number $3-4i$ ?

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Answer 1 · 2018-03-22T08:53:43

The trigonometric form is $=5(cos(-0.93)+isin(-0.93))$

Any complex number

$z=a+ib$

can be converted to the polar form

$z=|z|(costheta+i sintheta)$

Where,

$costheta=a/(|z|)$

and

$sintheta=b/(|z|)$

Here,

$z=3-4i$

$|z|=sqrt((3)^2+(-4)^2)=sqrt25=5$

$costheta=3/5=0.6$

$sintheta=-4/5=-0.8$

Therefore,

$theta=arcsin(-0.8)=-0.93rad$ , $[mod 2pi]$

$z=5(cos(-0.93)+isin(-0.93))$

How do I find the trigonometric form of the complex number 3-4i3-4i?