What is e^{i(pi/2)} ?

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

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simplify e^{i(pi/2)}

simplify

e^{i (\frac{π}{2})}

i

Solution steps

e^{i (\frac{π}{2})}

Remove parentheses:

(a) = a

= 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

14 x + 11 < - 31

\frac{9}{2} + \frac{5}{15}

\frac{8 ( 14 - 9 ) + 5}{3 ^{2} + 6}

9 x - 14 \leq 4 x - 15

\frac{1}{x + 5} > - 4