What is the value of sqrt(2)(cos((5pi)/4)+isin((5pi)/4)) ?

The value of sqrt(2)(cos((5pi)/4)+isin((5pi)/4)) is -1-i

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sqrt(2)(cos((5pi)/4)+isin((5pi)/4))

2 (cos (\frac{5 π}{4}) + i sin (\frac{5 π}{4}))

- 1 - i

Solution steps

2 (cos (\frac{5 π}{4}) + i sin (\frac{5 π}{4}))

Rewrite using trig identities:

cos (\frac{5 π}{4}) = - \frac{2}{2}

Rewrite using trig identities:

sin (\frac{5 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

tan (\frac{- 5 π}{3})

e^{\frac{π}{2}} - e^{a r c t a n (1 + 0^{2})}

\frac{8}{tan ( 7 0 ^{\circ} )}

arcsin (\frac{6}{18})

sin (arcsin (\frac{4}{5}) - arctan (\frac{5}{12}))

What is the value of sqrt(2)(cos((5pi)/4)+isin((5pi)/4)) ?
The value of sqrt(2)(cos((5pi)/4)+isin((5pi)/4)) is -1-i