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

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

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

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

- 1 - 3 i

Solution steps

2 (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}

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

Simplify

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

= - 1 - 3 i

arccsc (\frac{- 2}{3})

- \frac{1}{sin ^{2} ( 6 0 ^{\circ} )}

- 2 sin (2 (\frac{π}{4}))

sin (arctan (\frac{3}{2}))

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

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