Thread: Linear Algebra Proof

Question:
Suppose a and b are real numbers, not both 0. Find real numbers c and d such that 1/(a+bi)=c+di. (i as in the imaginary number.)


So far I have reworked the equation into

1=ac+adi+cbi-bd.

Not sure where to go from here. Just need a little push in the right direction. THANKS!!!

Originally Posted by eg37se

Question:
Suppose a and b are real numbers, not both 0. Find real numbers c and d such that 1/(a+bi)=c+di. (i as in the imaginary number

$\displaystyle \frac{1}
{{x + iy}} = \frac{{x - iy}}
{{x^2 + y^2 }}$

Thanks!!!.