What is the value of -3(cos((3pi)/4)+isin((3pi)/4)) ?

The value of -3(cos((3pi)/4)+isin((3pi)/4)) is (3sqrt(2))/2-i(3sqrt(2))/2

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-3(cos((3pi)/4)+isin((3pi)/4))

- 3 (cos (\frac{3 π}{4}) + i sin (\frac{3 π}{4}))

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

Solution steps

- 3 (cos (\frac{3 π}{4}) + i sin (\frac{3 π}{4}))

Use the following trivial identity:

cos (\frac{3 π}{4}) = - \frac{2}{2}

Use the following trivial identity:

sin (\frac{3 π}{4}) = \frac{2}{2}

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

Simplify

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

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

sin (\frac{π}{2} 2)

arctan (\frac{2.3}{5.3})

arctan (\frac{85}{167})

\frac{arcsin ( 0 )}{2}

3 sin (\frac{π}{12})

What is the value of -3(cos((3pi)/4)+isin((3pi)/4)) ?
The value of -3(cos((3pi)/4)+isin((3pi)/4)) is (3sqrt(2))/2-i(3sqrt(2))/2