What is the value of cos((5pi)/4)+isin((5pi)/4) ?

The value of cos((5pi)/4)+isin((5pi)/4) is -(sqrt(2))/2-i(sqrt(2))/2

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cos((5pi)/4)+isin((5pi)/4)

cos (\frac{5 π}{4}) + i sin (\frac{5 π}{4})

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

Solution steps

cos (\frac{5 π}{4}) + i sin (\frac{5 π}{4})

Rewrite using trig identities:

cos (\frac{5 π}{4}) = - \frac{2}{2}

Rewrite using trig identities:

sin (\frac{5 π}{4}) = - \frac{2}{2}

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

Simplify

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

cos (1) + i sin (1)

3 cos (13 5^{\circ})

1 - 2 sin^{2} (\frac{π}{7})

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

tan (5 3^{\circ}) \cdot 24

What is the value of cos((5pi)/4)+isin((5pi)/4) ?
The value of cos((5pi)/4)+isin((5pi)/4) is -(sqrt(2))/2-i(sqrt(2))/2