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

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

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

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

- \frac{1}{2} - i \frac{3}{2}

Solution steps

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}

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

Simplify

= - \frac{1}{2} - i \frac{3}{2}

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

cos (arcsin (\frac{2}{5}))

\frac{sin ( 3 π )}{2}

- tan (1)

8 \cdot sin (6 0^{\circ})

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