Question

if a+ib/c+id=p+iq then proove that a-ib/c-id =p-iq

Answer 1

Answer:

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

To prove that: $\frac{a-ib}{c-id} =p-iq$

Proof:

Let as assmune the complex numbers as

$z = p+iq\\\ z_1=a+ib\\\ z_2=c+id$

Then by the peoperties of complex numbers, we know that

If $z=\frac{z_1}{z_2}$

then $\bar z=\frac{\bar z_1}{\bar z_2}$

Where, $\bar z, \bar z_1 \text{ and } \bar z_2$ are the conjugate of complex numbers $z, z_1 \text{ and } z_2$

Here

$\bar z=p-iq$

$\bar z_1=a-ib$

$\bar z_2=c-id$

Thus

$\frac{a-ib}{c-id} =p-iq$            (Proved)