Hello.
I'm stuck with transposing a formula.
D = real(pr) / sqrt( real(pr)^2 + imag(pr)^2)
If I know D and Imag(pr) how do I find Real(pr)?
Many thanks
Albert
D = real(pr) / sqrt( real(pr)^2 + imag(pr)^2)
Multiply both sides by the denominator of the right side:
d (sqrt( real(pr)^2 + imag(pr)^2) = real(pr)
Square both sides:
d^2 * (real(pr)^2 + imag(pr)^2) = real(pr)^2
Distribute:
d^2 * real(pr)^2 + d^2 * imag(pr)^2 = real(pr)^2
Regroup:
d^2 * real(pr)^2 - real(pr)^2 = -d^2 * imag(pr)^2
Factor:
real(pr)^2 (d^2 - 1) = -d^2 * imag(pr)^2
Divide by (d^2 - 1):
real(pr)^2 = (-d^2 * imag(pr)^2) / (d^2 - 1)
Sqrt both sides:
real(pr) = +/- sqrt[ (-d^2 * imag(pr)^2) / (d^2 - 1) ]
Algebra 1 really.