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

The value of sqrt(2)(cos(pi/4)+isin(pi/4)) is 1+i

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

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

1 + 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}) : 1 + i

= 1 + i

sec (- \frac{9 π}{4})

- 2 cos (\frac{5 π}{6})

sec (\frac{- 2 π}{3})

8 cos (4 0^{\circ})

7 cos (5 0^{\circ})

What is the value of sqrt(2)(cos(pi/4)+isin(pi/4)) ?
The value of sqrt(2)(cos(pi/4)+isin(pi/4)) is 1+i