What is the value of (-sqrt(3)+i)(1/8 (cos((5pi)/3)+isin((5pi)/3))) ?

The value of (-sqrt(3)+i)(1/8 (cos((5pi)/3)+isin((5pi)/3))) is i/4

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(-sqrt(3)+i)(1/8 (cos((5pi)/3)+isin((5pi)/3)))

(- 3 + i) (\frac{1}{8} (cos (\frac{5 π}{3}) + i sin (\frac{5 π}{3})))

\frac{i}{4}

Solution steps

(- 3 + i) (\frac{1}{8} (cos (\frac{5 π}{3}) + i sin (\frac{5 π}{3})))

= (- 3 + i) \frac{1}{8} (cos (\frac{5 π}{3}) + i sin (\frac{5 π}{3}))

Rewrite using trig identities:

cos (\frac{5 π}{3}) = \frac{1}{2}

Rewrite using trig identities:

sin (\frac{5 π}{3}) = - \frac{3}{2}

= (- 3 + i) \frac{1}{8} (\frac{1}{2} + i (- \frac{3}{2}))

Simplify

(- 3 + i) \frac{1}{8} (\frac{1}{2} + i (- \frac{3}{2})) : \frac{i}{4}

= \frac{i}{4}

arccos (\frac{2}{4})

sin (\frac{25 π}{3})

cos (2 (\frac{π}{3}))

sin (23)

0.75 - cos (0.75)

What is the value of (-sqrt(3)+i)(1/8 (cos((5pi)/3)+isin((5pi)/3))) ?
The value of (-sqrt(3)+i)(1/8 (cos((5pi)/3)+isin((5pi)/3))) is i/4