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

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

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

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

3 + 3 i

Solution steps

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

Simplify

23 (cos (- \frac{5 π}{3}) + i sin (- \frac{5 π}{3})) : 23 cos (- \frac{5 π}{3}) + 23 i sin (- \frac{5 π}{3})

= 23 cos (- \frac{5 π}{3}) + 23 i sin (- \frac{5 π}{3})

Use the following property:

sin (- x) = - sin (x)

sin (- \frac{5 π}{3}) = - sin (\frac{5 π}{3})

= 23 cos (- \frac{5 π}{3}) + 23 i (- sin (\frac{5 π}{3}))

Use the following property:

cos (- x) = cos (x)

cos (- \frac{5 π}{3}) = cos (\frac{5 π}{3})

= 23 cos (\frac{5 π}{3}) + 23 i (- sin (\frac{5 π}{3}))

Simplify

= 23 cos (\frac{5 π}{3}) - 23 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}

= 23 \frac{1}{2} - 23 i (- \frac{3}{2})

Simplify

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

= 3 + 3 i

- cos (1 7^{\circ})

arctan (\frac{0.016}{0.025})

arccos^{2} (1)

51 tan (1 5^{\circ})

- 2 sec (2 (\frac{3 π}{4}))

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