What is the value of 2(cos(45)+isin(45)) ?

The value of 2(cos(45)+isin(45)) is sqrt(2)+sqrt(2)i

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2(cos(45)+isin(45))

2 (cos (4 5^{\circ}) + i sin (4 5^{\circ}))

2 + 2 i

Solution steps

2 (cos (4 5^{\circ}) + i sin (4 5^{\circ}))

Use the following trivial identity:

cos (4 5^{\circ}) = \frac{2}{2}

Use the following trivial identity:

sin (4 5^{\circ}) = \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

π cos (π) + sin (π)

- 8 sin (0)

2 cos (\frac{5 π}{4})

sin (arcsin (\frac{3}{5}) + arccos (- \frac{8}{17}))

arcsin (\frac{21}{29})

What is the value of 2(cos(45)+isin(45)) ?
The value of 2(cos(45)+isin(45)) is sqrt(2)+sqrt(2)i