What is the value of 6(cos((4pi)/3)+isin((4pi)/3)) ?

The value of 6(cos((4pi)/3)+isin((4pi)/3)) is -3-3sqrt(3)i

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6(cos((4pi)/3)+isin((4pi)/3))

6 (cos (\frac{4 π}{3}) + i sin (\frac{4 π}{3}))

- 3 - 33 i

Solution steps

6 (cos (\frac{4 π}{3}) + i sin (\frac{4 π}{3}))

Rewrite using trig identities:

cos (\frac{4 π}{3}) = - \frac{1}{2}

Rewrite using trig identities:

sin (\frac{4 π}{3}) = - \frac{3}{2}

= 6 (- \frac{1}{2} + i (- \frac{3}{2}))

Simplify

6 (- \frac{1}{2} + i (- \frac{3}{2})) : - 3 - 33 i

= - 3 - 33 i

221 cos (5 5^{\circ})

- (- 1)^{3} - cos (- 1)

50 tan (7 0^{\circ})

11 sin (6 0^{\circ})

cos (2 arcsin (\frac{12}{13}))

What is the value of 6(cos((4pi)/3)+isin((4pi)/3)) ?
The value of 6(cos((4pi)/3)+isin((4pi)/3)) is -3-3sqrt(3)i