Simple question: Use Euler's formula to rewrite an expression

DWill
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Homework Statement


Use Euler's formula to write the given expression in the form a + ib:

e^(2-(pi/2)i)


Homework Equations


Euler's formula: e^(it) = cos(t) + i*sin(t)


The Attempt at a Solution


I'm not sure how to get started on this one... am I supposed to get the expression into the e^(it) form somehow first?
 
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Use the laws of exponentials to split it into e^2*e^(-i*pi/2) first. Now use Euler's formula on the second factor. The first one you know well.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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