How do you write the trigonometric form of $-3-i$ ?

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Answer 1 · 2017-08-01T13:44:06

The trigonometric form is $=sqrt10(cos198.4^@+isin198.4^@)$

Let $z=-3-i$

The trigonometris form is

$z=r(costheta+isintheta)$

If $z=a+ib$

$z=|z|(a/|z|+b/|z|i)$

The modulus is

$|z|=sqrt(a^2+b^2)=sqrt((-3)^2+(-1)^2)=sqrt10$

Therefore,

$z=sqrt10(-3/sqrt10-1/sqrt10i)$

$costheta=-3/sqrt10$

and

$sintheta=-1/sqrt10$

We are in the quadrant $III$

$theta=198.4^@$

Therefore,

$z=sqrt10(cos198.4^@+isin198.4^@)=e^(i198.4^@)$

How do you write the trigonometric form of -3-i-3-i?