What is e^{(2pii)/4} ?

The solution to e^{(2pii)/4} is i

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simplify e^{(2pii)/4}

simplify

e^{\frac{2 πi}{4}}

i

Solution steps

e^{\frac{2 πi}{4}}

\frac{2 πi}{4} = \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

36 x^{2} - 12 x + 1 = 4

t^{2} + 8 t

x^{2} + 5 x - 20 = 0

1^{2} + b^{2} = 2^{2}

x - 3 = 2 + x