Question

If $\frac{a+ib}{c+id}=p+iq$ then $\frac{a-ib}{c-id}=p-iq$

• A. True
• B. False

Answer 1

The correct option is A True

Given $p+iq=\frac{a+ib}{c+id}$

applying modulus on both sides

$|p+iq|=\frac{|a+ib|}{|c+id|}$

$⟹\sqrt{p^2+q^2}=\frac{\sqrt{a^2+b^2}}{\sqrt{c^2+d^2}}$

Squaring on both sides

$p^2+q^2=\frac{a^2+b^2}{c^2+d^2}$

$(p+iq)(p-iq)=\frac{(a+ib)(a-ib)}{(p+iq)(p-iq)}$

$⟹p-iq=\frac{a-ib}{c-id}$