Find the argument of $(-sqrt3 +i)^8$ ?

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Answer 1 · 2017-04-02T15:34:15

Argument is $(2pi)/3$

$(-sqrt3 +i)^8$

= $[2(-sqrt3/2+ixx1/2)]^8$

= $[2(cos((5pi)/6)+isin((5pi)/6))]^8$

Now according to DeMoivre's Theorem

$(r(costheta+isintheta))^n=r^n(cosntheta+isinntheta)$

Hence $[2(cos((5pi)/6)+isin((5pi)/6))]^8$

= $[2^8(cos((5pi)/6xx8)+isin((5pi)/6xx8))]$

= $256(cos((20pi)/3)+isin((20pi)/3))$

= $256(cos(6pi+(2pi)/3)+isin(6pi+(2pi)/3))$

= $256(cos((2pi)/3)+isin((2pi)/3))$

Hence while modulus of $(-sqrt3 +i)^8$ is $256$ , argument is $(2pi)/3$

Find the argument of (-sqrt3 +i)^8(-sqrt3 +i)^8?