# complex numbers

• Oct 24th 2009, 05:14 AM
alexandrabel90
complex numbers
how do you solve

(7+24i)/(x+iy)^2 = 1?

i got x= 4i or x=-4i or x=3 or x=-3...
but the answer is x =4, y=3 or x=-4, y=-3

thanks!
• Oct 24th 2009, 05:30 AM
mr fantastic
Quote:

Originally Posted by alexandrabel90
how do you solve

(7+24i)/(x+iy)^2 = 1?

i got x= 4i or x=-4i or x=3 or x=-3...
but the answer is x =4, y=3 or x=-4, y=-3

thanks!

$7 + 24i = x^2 - y^2 + 2xy i$.

Therefore:

$7 = x^2 - y^2$ .... (1)

$24 = 2xy$ .... (2)

Solve simultaneously for x and y.
• Oct 24th 2009, 05:40 AM
tonio
Quote:

Originally Posted by alexandrabel90
how do you solve

(7+24i)/(x+iy)^2 = 1?

i got x= 4i or x=-4i or x=3 or x=-3...
but the answer is x =4, y=3 or x=-4, y=-3

thanks!

$\frac{7+24i}{(x+iy)^2}=1 \Longrightarrow x^2-y^2+2xyi=7+24i$

Try to take it from here equating real and imaginary parts and choosing wisely the sign of solutions...

Tonio