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

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

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

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

- 1 + 3 i

Solution steps

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

Use the following trivial identity:

cos (\frac{2 π}{3}) = - \frac{1}{2}

Use the following trivial identity:

sin (\frac{2 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

\frac{8.3}{tan ( 1 6 ^{\circ} )}

cos (3 0^{\circ} + 4 5^{\circ})

9 sin (6 0^{\circ})

3 sin (- \frac{π}{2})

1 cos (4 5^{\circ})

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