- #1
vkash
- 318
- 1
Homework Statement
(z' represent conjugate of complex number z,i is iota =sqrt(-1))
(1)find the locus of z.
|z|2+4z'=0
(2)|z1|=1, |z2|=2, then find the value of |z1-z2|2+|z1+z2|2
(3)z=(k+3)+i[sqrt(3-k2)] for all real k. find locus of z
Homework Equations
|z|2=z.z'
The Attempt at a Solution
(1) |z|2+4z'= |z|2+4z'*z/z
|z|2{1+4/z}=0
it is possible iff z= -4. so it has one solution.
(2) I take z1= cos(a)+i sin(a) and z2=2{cos(b)+i*sin(b)}
after putting these values in the required equation i got 10.
(3) let z=x+iy
x=k+3; y=sqrt(3-k2)
x-3=k; y2=3-k2
squaring x and adding it to y2,
(x-3)2+y2=k2+3-k2
that's circle.
unfortunately all of my answers are incorrect.
I want to know why?