Complex number(exponential form)

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Let z = 4e^i(pi/6)
find iz and |e^iz|

what is iz?
is it imaginary part of z?
 
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No, "iz" is exactly what it looks like: i times z. The difficulty appears to be that z is in polar form while i is in "rectangluar" form. Either write i in polar form or write z in rectangular form. Then multiply.
 
HallsofIvy said:
No, "iz" is exactly what it looks like: i times z. The difficulty appears to be that z is in polar form while i is in "rectangluar" form. Either write i in polar form or write z in rectangular form. Then multiply.

what bout the second part?
 
naspek said:
what bout the second part?
That was what I meant when I said "Either write i in polar form or write z in rectangular form. Then multiply." What is i in polar form? What is z in rectangular form?
 

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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