What is the trigonometric form of $(-6+9i)$ ?

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Answer 1 · 2018-06-01T12:14:18

In trigonometric form expressed as
$sqrt117(cos(123.69)+isin(123.69))$

$Z=a+ib$ . Modulus: $|Z|=sqrt (a^2+b^2)$ ;

Argument: $theta=tan^-1(b/a)$ Trigonometrical form :

$Z =|Z|(costheta+isintheta)$

$Z=(-6+9i)$ . Modulus $|Z|=sqrt((-6 )^2+9^2)= sqrt 117$

Argument: $tan alpha= 9/6=3/2:. alpha=tan^-1 (3/2)=56.31^0$

Z lies on second quadrant, so , $theta =180-alpha$

$:. theta= 180-56.31=123.69^0$

:. $Z=sqrt117(cos(123.69)+isin(123.69))$

In trigonometric form expressed as

$sqrt117(cos(123.69)+isin(123.69))$ [Ans]

What is the trigonometric form of (-6+9i) (-6+9i) ?