What is the value of 2(cos((5pi)/3)+isin((5pi)/3)) ?

The value of 2(cos((5pi)/3)+isin((5pi)/3)) is 1-sqrt(3)i

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2(cos((5pi)/3)+isin((5pi)/3))

2 (cos (\frac{5 π}{3}) + i sin (\frac{5 π}{3}))

1 - 3 i

Solution steps

2 (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}

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

Simplify

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

= 1 - 3 i

cos (- 3 7^{\circ})

arccos (0.5625)

csch (- 0.5)

arctan (\frac{20}{13})

sin^{2} (3 0^{\circ}) - cos^{2} (3 0^{\circ})

What is the value of 2(cos((5pi)/3)+isin((5pi)/3)) ?
The value of 2(cos((5pi)/3)+isin((5pi)/3)) is 1-sqrt(3)i