Complex Analysis Answers

Q. Find locus of points in plane satisfying given conditions.
(i) │z-1│=6
(ii) │z+3│+│z+1│= 4
(iii) Arg z=π/3
(iv) Arg(z-1) =-3 π/4

solve the following equation and find the values of x and y:

jx/(1+jy) = (3x+j4)/(x+3y)

Find the number of solutions to the equation z^2 + |z|^2 = 0.

Find all z,such that z^(2015)=321

please help me with this question
http://i12.photobucket.com/albums/a219/an_nguyen16/homework2_zpsivj9qhrv.jpg

A circle in the z-plane has its center at z=3 and a radius of a radius of 2 units. Determine its image in w-plane when transformed by w=1/2.

How can we draw graph 8+6i on grap ?

Find the fifth roots of 32(cos 280° + i sin 280°).

If a complex number lies in the third quadrant, then where does its conjugate lie in?

does multiplication of two imaginary numbers imaginary or real? if i multiply 2i and 3i then it is = -6 which is real .if √-3 and √-2 are multiplied then it gives - √6 which is real . but if i do the same thing like this √-3 * √-2 =√{(-3)*(-2)} =√6 which is also real . so why the ans is -√6 . we know multiplication of two complex numbers is a complex number . if i write 2i as (0+2i) and 3i as (0+3i) and then multiply these two should come a complex number as definition . but why it's real?