What is e^{(ipi)/2} ?

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

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simplify e^{(ipi)/2}

simplify

e^{\frac{iπ}{2}}

i

Solution steps

e^{\frac{iπ}{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

ab + b c + b^{2} + a c

4 b^{2} + 8 b + 7 = 4

5 x^{2} + 12 x < 9

8 t^{4} - 32 t^{3} + t - 4

3 m^{2} + 11 mn + 6 n^{2}