What is the value of 4(cos(45)+isin(45)) ?

The value of 4(cos(45)+isin(45)) is 2sqrt(2)+2sqrt(2)i

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4(cos(45)+isin(45))

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

22 + 22 i

Solution steps

4 (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}

= 4 (\frac{2}{2} + i \frac{2}{2})

Simplify

4 (\frac{2}{2} + i \frac{2}{2}) : 22 + 22 i

= 22 + 22 i

arccos (\frac{18}{25})

2 cos (2 - π)

cos (100 0^{\circ})

cos (11 8^{\circ})

- 0 cos (0) + sin (0)

What is the value of 4(cos(45)+isin(45)) ?
The value of 4(cos(45)+isin(45)) is 2sqrt(2)+2sqrt(2)i