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

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Answer 1 · 2018-06-01T12:14:18

In trigonometric form expressed as
$\sqrt{117} (cos (123.69) + i sin (123.69))$ $sqrt117(cos(123.69)+isin(123.69))$

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

Argument: $θ = {tan}^{- 1} (\frac{b}{a})$ $theta=tan^-1(b/a)$ Trigonometrical form :

$Z = | Z | (cos θ + i sin θ)$ $Z =|Z|(costheta+isintheta)$

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

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) (-6+9i) ?