What is the value of [2(cos(pi/3)+isin(pi/3))]^4 ?

The value of [2(cos(pi/3)+isin(pi/3))]^4 is (1+sqrt(3)i)^4

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[2(cos(pi/3)+isin(pi/3))]^4

[2 (cos (\frac{π}{3}) + i sin (\frac{π}{3}))]^{4}

(1 + 3 i)^{4}

Solution steps

[2 (cos (\frac{π}{3}) + i sin (\frac{π}{3}))]^{4}

= (2 (cos (\frac{π}{3}) + i sin (\frac{π}{3})))^{4}

Use the following trivial identity:

cos (\frac{π}{3}) = \frac{1}{2}

Use the following trivial identity:

sin (\frac{π}{3}) = \frac{3}{2}

= (2 (\frac{1}{2} + i \frac{3}{2}))^{4}

Simplify

(2 (\frac{1}{2} + i \frac{3}{2}))^{4} : (1 + 3 i)^{4}

= (1 + 3 i)^{4}

\frac{5}{sin ( 4 0 ^{\circ} )}

sin (arcsin (\frac{5}{13}) + arccos (- \frac{7}{25}))

cos (π) π

2 tan (- 2)

300 sin (2 0^{\circ})

What is the value of [2(cos(pi/3)+isin(pi/3))]^4 ?
The value of [2(cos(pi/3)+isin(pi/3))]^4 is (1+sqrt(3)i)^4