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

The value of sqrt(2)(cos(45)+isin(45)) is 1+i

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

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

1 + 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}) : 1 + i

= 1 + i

4 (sin (4) + cos (4) + 4 (cos (4) - sin (4)))

2 cos^{2} (1)

cos (arcsin (\frac{3}{7}))

- 3.5 \cdot 3.5 \cdot sin (3.5 \cdot 2.4 - 0.8)

\frac{120}{tan ( 2 4 ^{\circ} )}

What is the value of sqrt(2)(cos(45)+isin(45)) ?
The value of sqrt(2)(cos(45)+isin(45)) is 1+i