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

The value of (2(cos(pi/3)+isin(pi/3)))^3 is -8

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(2(cos(pi/3)+isin(pi/3)))^3

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

- 8

Solution steps

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

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}))^{3}

Simplify

(2 (\frac{1}{2} + i \frac{3}{2}))^{3} : - 8

= - 8

cos (- 6 0^{\circ}) \cdot sin (- 24 0^{\circ})

coth (ln (7))

sec (0.02) ln (0.96)

cos (\frac{π}{3}) cos (\frac{π}{6}) - sin (\frac{π}{3}) sin (\frac{π}{6})

sin (\frac{π}{3} - arcsin (- \frac{1}{2}))

What is the value of (2(cos(pi/3)+isin(pi/3)))^3 ?
The value of (2(cos(pi/3)+isin(pi/3)))^3 is -8