What is e^{pisqrt(2)(1+i)} ?

The solution to e^{pisqrt(2)(1+i)} is e^{sqrt(2)pi}cos(sqrt(2)pi)+ie^{sqrt(2)pi}sin(sqrt(2)pi)

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simplify e^{pisqrt(2)(1+i)}

simplify

e^{π 2 (1 + i)}

e^{2 π} cos (2 π) + i e^{2 π} sin (2 π)

Solution steps

e^{π 2 (1 + i)}

Apply imaginary number rule:

e^{a + ib} = e^{a} (cos (b) + i sin (b))

= e^{2 π} (cos (2 π) + i sin (2 π))

Rewrite

e^{2 π} (cos (2 π) + sin (2 π) i)

in standard complex form:

e^{2 π} cos (2 π) + e^{2 π} sin (2 π) i

= e^{2 π} cos (2 π) + e^{2 π} sin (2 π) i

so l v e (x^{2} + 4 x - 5)

\frac{- 250 x ^{3} + 600 x ^{2} - 480 x + 129}{( 4 - 5 x ) ^{3}}

(y^{4} - 2 x y) d x + 3 x^{2} d y

(cosh (x) + sinh (x))^{3}

What is e^{pisqrt(2)(1+i)} ?
The solution to e^{pisqrt(2)(1+i)} is e^{sqrt(2)pi}cos(sqrt(2)pi)+ie^{sqrt(2)pi}sin(sqrt(2)pi)