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

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

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

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

1 + 3 i

Solution steps

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

Simplify

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

= 1 + 3 i

tan (33.6 9^{\circ})

\frac{tan ( 6 0 ^{\circ} ) sin ( 3 0 ^{\circ} )}{cos ( 6 0 ^{\circ} )}

- sin (\frac{7 π}{2})

\frac{1 - cos ( - 0.1 )}{- 0.1}

cos (56.3 1^{\circ})

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