What is the trigonometric form of $(-4+3i)$ ?

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Answer 1 · 2016-04-18T14:30:08

$5costheta+i5sintheta$ , where $theta=tan^(-1)(-3/4)$

Trigonometric form of a complex number $a+bi$ is $rcostheta+isintheta$ .

As such here, $rcostheta=-4$ and $rsintheta=3$ .

Squaring the two and adding

$r^2(cos^2theta+sin^2theta)=(-4)^2+3^2=16+9=25$

or $r^2=25$ and $r=5$

Dividing we get $(rsintheta)/(rcostheta)=$ -3/4# or

$tantheta=-3/4$ or $theta=tan^(-1)(-3/4)$

Hence $a+bi$ in trigonometric form is $5costheta+i5sintheta$ , where $theta=tan^(-1)(-3/4)$

What is the trigonometric form of (-4+3i) (-4+3i) ?