# Complex analysis

• Apr 2nd 2008, 12:57 AM
sasom
Complex analysis
Hi.

I have a problem with my homework. I can't solve this function:

f(z)= (az + b)/(cz + d)

which transfers -1-2i -> -5i, 3 -> 1+5i and -4-3i -> -4+3i

and then calculate w=f(-6-5i).

I've tried to solve this problem for three times and I still haven't got the right resultat. Please help me! bye
• Apr 2nd 2008, 03:57 AM
mr fantastic
Quote:

Originally Posted by sasom
Hi.

I have a problem with my homework. I can't solve this function:

f(z)= (az + b)/(cz + d)

which transfers -1-2i -> -5i, 3 -> 1+5i and -4-3i -> -4+3i

and then calculate w=f(-6-5i).

I've tried to solve this problem for three times and I still haven't got the right resultat. Please help me! bye

Solve the following two equations for a, b, c and d:

$\displaystyle -5i = \frac{a(-1-2i) + b}{c(-1 - 2i) + d}$ .... (1)

$\displaystyle -4 + 3i = \frac{a(-4 + 3i) + b}{c(-4 + 3i) + d}$ .... (2)

If you have attemped this, please show your working.
• Apr 2nd 2008, 04:18 AM
sasom
hey

I got this:

a(-75/29 -57/29i)+ c(457/29 + 171/29i)= 0
• Apr 2nd 2008, 05:06 AM
mr fantastic
Quote:

Originally Posted by sasom
hey

I got this:

a(-75/29 -57/29i)+ c(457/29 + 171/29i)= 0

Let me re-word my request: