Complex Analysis Answers

Calculate z^6=64

If w=3iz-z2 given that z=x+iy, find w2 in terms of xand y.

Select one:

A x4+y4+2x2y2-6x2y-6y3-9x2-9y2

B x4+y4+2x2y2-6x2y-6y3+9x2+9y2

C x4+y4+2x2y2-6x2y-6y3+9x2-9y2

D x4-y4+2x2y2-6x2y-6y3+9x2+9y2

Find square root of 1+i

Find two different linear mappings which map imz>3 onto rez>3

obtain first three terms of taylors series for f(z) = sin z about 2=0

Obtain first three terms of taylors series for f(z) = sin z about z =0

Find the square root of −5 − 12𝑖

Evaluate ∫f 𝑜𝑣𝑒𝑟 𝑐 where 𝑓( 𝑧 )= 𝑥^2 + 𝑖𝑦^2 where c is given by 𝑧 (𝑡 )= 𝑡^2 + 𝑖𝑡^2, 0 ≤ 𝑡 ≤ 1

Show that 𝑠𝑖𝑛𝑖𝑦 = 𝑖 𝑠𝑖𝑛hy

Using the Cauchy –Riemann equations verify the following is analytic or not

i) 𝑥^2 − 𝑦^2 + 2𝑖𝑥𝑦

ii) 𝑥^2 + 𝑦^2 − 2𝑖𝑥𝑦