What is the trigonometric form of $(-5+12i)$ ?

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Answer 1 · 2016-01-04T20:57:42

13 ( cos1.96 +isin1.96)

the complex number z = x + iy can be written in trigonemetric form as $z = r( costheta + isintheta)$

the modulus r = $sqrt(x^2 + y^2)$

and the argument $theta$ is found by using

$tantheta = y/x$

in this case $r = sqrt ((-5)^2 +(12)^2)$

$= sqrt (25 + 144 ) = sqrt169 = 13$

$tanalpha = y/x = 12/5 =2.4$ and so

$alpha = 1. 176$

arg z = $( pi - 1.176 )$ = 1.96

In this case z is in the 2nd quadrant and so the required argument is $( pi - alpha)$

What is the trigonometric form of (-5+12i) (-5+12i) ?