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

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

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

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

- 2 + 2 i

Solution steps

2 (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}

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

Simplify

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

= - 2 + 2 i

58 sin (5 4^{\circ})

\frac{67}{sin ( 4 5 ^{\circ} )}

tan (\frac{π}{4}) - sin (\frac{π}{6})

sec (- 31 0^{\circ})

15 sin (2 5^{\circ})

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