Question

Find c and d so that (5-7i)(c+di)=1

Answer 1

When I FOIL it out, I get 5c+5di-7ci-7di^2=1
But I don't know where to go from there...

Answer 2

i^2 = -1

Answer 3

i^2 means -1
and then equate the real and imaginary parts

Answer 4

yup..

Answer 5

So... 5c+5di-7ci+7d=1?

Answer 6

Yes.
Now, write that left side so you separate the real and imaginary parts:
(5c + 7d) + (5d - 7c)i = 1
For this equality to be true, 2 things must be true.
The real part has to be 1, and the imaginary part 0.
So, 5c + 7d = 1 and 5d - 7c = 0
Solve that set of equations and you're done.

Answer 7

Thank you! My teacher didn't explain it that well so I couldn't understand it...