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

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

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

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

2 + 23 i

Solution steps

4 (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}

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

Simplify

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

= 2 + 23 i

sec (\frac{5}{4} π)

cot (3 3^{\circ})

cos (2 π) + 1

sin (\frac{π}{4}) + tan (\frac{π}{6})

2 cos (\frac{π}{6}) - 4 sin (\frac{π}{6})

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