What is the trigonometric form of $-1+3i$ ?

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Answer 1 · 2018-02-20T10:59:28

The trignometric form is $z=sqrt(10)(cos(108.4^@)+isin(108.4^@))$ , $[mod 360^@]$

The complex number is

$z=-1+3i$

The polar form of $z=a+ib$

is

$z=r(costheta+isintheta)$

Where,

$r=|z|$

$costheta=a/|z|$

$sintheta=b/|z|$

Here,

$|z|=r=sqrt((-1)^2+(3)^2)=sqrt(10)$

$costheta=-1/sqrt(10)$

$sintheta=3/sqrt(10)$

$theta=108.4^@$

Therefore,

$z=sqrt(10)(cos(108.4^@)+isin(108.4^@))$ , $[mod 360^@]$

What is the trigonometric form of -1+3i-1+3i?