What is the value of 3(cos(120)+isin(120)) ?

The value of 3(cos(120)+isin(120)) is -3/2+i(3sqrt(3))/2

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3(cos(120)+isin(120))

3 (cos (12 0^{\circ}) + i sin (12 0^{\circ}))

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

Solution steps

3 (cos (12 0^{\circ}) + i sin (12 0^{\circ}))

Use the following trivial identity:

cos (12 0^{\circ}) = - \frac{1}{2}

Use the following trivial identity:

sin (12 0^{\circ}) = \frac{3}{2}

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

Simplify

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

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

sin (4 \frac{π}{3})

sin (4 \frac{π}{4})

sin (103 5^{\circ})

sin^{4} (9 0^{\circ})

6 + 3 cos (0)

What is the value of 3(cos(120)+isin(120)) ?
The value of 3(cos(120)+isin(120)) is -3/2+i(3sqrt(3))/2