Question

a+3i/2+ib=1-i show that 5a -7b =0

Answer 1

Given $\frac{a+3i}{2+ib} =1-i$. This equation can be written as

$a+3i=(1-i)(2+ib)\\ a+3i=2+b+i(b-2)$

Equating real and imaginary parts,

$a=2+b\\ 3=b-2\\ b=5\\ a=7$

So, $5a-7b=35-35=0$. Proof is complete.

Answer 2

Answer:

Step-by-step explanation:

a+3i =(1-i)(2+ib)

       =2+ib-2i-bi^2

       =2+b+ib-2i

a+3i=2+b+ib-2i

By equality of complex numbers

a=2+b

3=b-2

b=3+2=5

Putting b=5

a=2+5=7

So complete this prove 5a-7b=0