- #1
Saladsamurai
- 3,020
- 7
Suppose that a and b are real numbers, not both 0. Find real numbers c and d such that
[tex]\frac{1}{a+bi}=c+di[/tex]
What do they mean find c & d? That's two unknowns is it not?
Anyway. My attempt:
[tex]\begin{array} \frac{1}/({a+bi})=c+di\\ \Rightarrow (a+bi)(c+di)=1\\\Rightarrow ac-bd+(ad+bc)i=1\\\Rightarrow \frac{1+bd-ac}{ad+bc}=i\end{array}[/tex]
Now I know that I could square both sides to get rid of i, but I am not sure how whether that will help or hurt.
[tex]\frac{1}{a+bi}=c+di[/tex]
What do they mean find c & d? That's two unknowns is it not?
Anyway. My attempt:
[tex]\begin{array} \frac{1}/({a+bi})=c+di\\ \Rightarrow (a+bi)(c+di)=1\\\Rightarrow ac-bd+(ad+bc)i=1\\\Rightarrow \frac{1+bd-ac}{ad+bc}=i\end{array}[/tex]
Now I know that I could square both sides to get rid of i, but I am not sure how whether that will help or hurt.