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

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

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

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

- 2 - 2 i

Solution steps

2 (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}

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

Simplify

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

= - 2 - 2 i

arcsin (\frac{4}{2})

cot (- 14 0^{\circ})

5 \cdot sin (\frac{2 π}{7})

6 cos (3)

cos (10 6^{\circ})

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