Question

help , complex analysis

Answer 1

What do you need help on?

Answer 2

Sorry, this is much too advanced for me..

Answer 3

@Mashy

Answer 4

You don't need contours integral here. You only need to know function composition and the trigonometric relations,
\[1+\tan^2\phi=\frac{1}{\cos^2\phi}\\
\sin\phi=\sqrt{1-\cos^2\phi}\]

Answer 5

i need contour cuz its complex :)
not real

Answer 6

but since u have an idea , can u solve it ?

Answer 7

first expand z = 2e^ix = 2(sinx + i*cosx) then use trigonometric formulae

Answer 8

Exactly.

Answer 9

there is no triagonometric formula :O
can u show it ?

Answer 10

\[z=2e^{i\theta}=2(\cos\theta+i\sin\theta)\]

Answer 11

Now calculate,
\[z(\arctan(\frac{y}{\sqrt{4-y^2}}))\]