The solution to e^{pi/2 i} is i

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simplify e^{pi/2 i}

Solution

simplify

e^{\frac{π}{2} i}

i

Solution steps

e^{\frac{π}{2} i}

Multiply

\frac{π}{2} i : \frac{πi}{2}

= e^{\frac{πi}{2}}

Apply imaginary number rule:

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

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

Use the following trivial identity:

cos (\frac{π}{2}) = 0

Use the following trivial identity:

sin (\frac{π}{2}) = 1

0 + 1 i = 1 i

= 1 i

Multiply:

1 i = i

= i

lo g_{10} (\frac{1}{100})

x^{2} > 25

3 r^{2} + 40 r + 100

ln (27)

27 p^{2} - 9 p + 18