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

The value of 4(cos((4pi)/3)+isin((4pi)/3)) is -2-2sqrt(3)i

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

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

- 2 - 23 i

Solution steps

4 (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}

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

Simplify

4 (- \frac{1}{2} + i (- \frac{3}{2})) : - 2 - 23 i

= - 2 - 23 i

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981 cos (3 0^{\circ})

\frac{1 + cos ( 7 5 ^{\circ} )}{2}

4 1 + cos^{2} (\frac{7 π}{32})

What is the value of 4(cos((4pi)/3)+isin((4pi)/3)) ?
The value of 4(cos((4pi)/3)+isin((4pi)/3)) is -2-2sqrt(3)i