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

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

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

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

2 + 2 i

Solution steps

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

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

Use the following trivial identity:

sin (\frac{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

3 cot^{2} (6 0^{\circ})

\frac{12}{cos ( 3 5 ^{\circ} )}

- \frac{1}{2} sin (0)

3.9 tan (1 8^{\circ})

- 4 π^{2} cos (\frac{5 π}{4})

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