complex number questions (1 Viewer)

[Loner]

I was having some trouble with the following questions. Can anyone help?

Find the value of the real numbers, x and y, in the following:

a. x / (1 + i) + y / (1 - 2i) = 1

b. x / (2 - i) + yi / (i - 3) = 2 / (1 + i)


Thanks in advance!

 

[haque]

For eascyh one realise the denominators and then group into imaginar and real parts-then equate real and imaginary parts(should give u simultenous equations)-solve it and u'll get the answer

 

[IceOnFire]

Since I don't want to make a thread just on my question, I will just post it here.

Describe the locus of:

arg(z-1) - arg(z+i) = pi/4

I know you can find this geometrically, but how do you find it algebratically?

Thanks in advance.

 

[haque]

The worst way u could do it(i don't mean to sound aggressive) is algebraic for this locus-however u could write it as
arg(z-1/z+i)=pi/4 then we can just say
z-1/z+i=kcis(pi/4) Since the angle between these two vectors is 45 degrees and one corresponds to the other being rotated anticlockwise by 45 degrees and perhaps enlarged by a facotr of k-u see these complications make the geometric method much better. u could then express z as x+iy and proceed algebraically

 

[SeDaTeD]

You are assuming that |z-1/z+i| = 1 when you say z-1/z+i=cis(pi/4). Try z-1/z+i=rcis(pi/4).

 

[haque]

Yea i know sorry late edit