If-x-iy-1-a-ib-prove-that-x-2-y-2-a-2-b-2-1-

Question Number 16917 by tawa tawa last updated on 28/Jun/17

If x + iy = \frac{1}{a + ib}

prove that : (x^{2} + y^{2}) (a^{2} + b^{2}) = 1

Answered by Tinkutara last updated on 28/Jun/17

x + i y = \frac{1}{a + i b}

x - i y = \frac{1}{a - i b}

x^{2} + y^{2} = \frac{1}{a^{2} + b^{2}}

Commented by tawa tawa last updated on 28/Jun/17

God bless you sir . but sir why (x - iy) = \frac{1}{(a - ib)}

Commented by Tinkutara last updated on 28/Jun/17

It is a rule for complex numbers : If

z = \frac{z_{1}}{z_{2}} then \bar{z} = \frac{{\bar{z}}_{1}}{{\bar{z}}_{2}}, where \bar{z} denotes

the conjugate of z .

Commented by tawa tawa last updated on 28/Jun/17

God bless you sir .