What is the value of 27(cos(pi/3)+isin(pi/3)) ?

The value of 27(cos(pi/3)+isin(pi/3)) is 27/2+i(27sqrt(3))/2

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

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

\frac{27}{2} + i \frac{27 3}{2}

Solution steps

27 (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}

= 27 (\frac{1}{2} + i \frac{3}{2})

Simplify

27 (\frac{1}{2} + i \frac{3}{2}) : \frac{27}{2} + i \frac{27 3}{2}

= \frac{27}{2} + i \frac{27 3}{2}

1 + 0.1 \cdot (\frac{1.2}{2}) \cdot tan^{2} (6 0^{\circ})

e^{\frac{π}{2}} cos (\frac{π}{2})

cos (0.86)

cos (0.83)

cos (\frac{39 π}{6})

What is the value of 27(cos(pi/3)+isin(pi/3)) ?
The value of 27(cos(pi/3)+isin(pi/3)) is 27/2+i(27sqrt(3))/2