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

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simplify e^{i pi/2}

Solution

simplify

e^{i \frac{π}{2}}

i

Solution steps

e^{i \frac{π}{2}}

Multiply

i \frac{π}{2} : \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

x^{2} - 12 x + 30 = 23

3 x - 5 > 7 x + 12

\frac{x ^{4} y ^{5}}{x ^{3} y ^{2}}

\frac{\frac{2}{x} - \frac{4}{y}}{\frac{- 5}{y} + \frac{3}{x}}

\frac{25 k - 15}{25 k + 40}