What is the value of 3(cos(30)+isin(30)) ?

The value of 3(cos(30)+isin(30)) is (3sqrt(3))/2+i 3/2

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3(cos(30)+isin(30))

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

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

Solution steps

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

Use the following trivial identity:

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

Use the following trivial identity:

sin (3 0^{\circ}) = \frac{1}{2}

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

Simplify

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

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

coth (ln (6))

1 - sin^{2} (0)

3 + 2 sin (- \frac{π}{4})

sin (2 \cdot 2 5^{\circ})

3 + 2 sin (- \frac{π}{2})

What is the value of 3(cos(30)+isin(30)) ?
The value of 3(cos(30)+isin(30)) is (3sqrt(3))/2+i 3/2