IIT-JEE 1979Question 1
If $x+iy=\sqrt{\dfrac{a+ib}{c+id}}$, prove that $\left(x^{2}+y^{2}\right)^{2}=\dfrac{a^{2}+b^{2}}{c^{2}+d^{2}}$.
Complex Numbers
Answerproved
Solution
Squaring moduli: $|x+iy|^2=\left|\frac{a+ib}{c+id}\right|=\sqrt{\frac{a^2+b^2}{c^2+d^2}}$, i.e. $x^2+y^2=\sqrt{\frac{a^2+b^2}{c^2+d^2}}$. Squaring gives $(x^2+y^2)^2=\frac{a^2+b^2}{c^2+d^2}$.