Question

If $\frac{a+3i}{2+ib}=1-i$, show that (5a - 7b) = 0.

Answer 1

Answer:

Step-by-step explanation:

Hi,

Given that (a + ib)/(2 + ib) = 1 - i

On cross multiplying with 2 + ib, we get

a + i3 = (1 - i)*(2 + ib)

= 2 + ib -2i + b

= (2 + b) + i(b - 2)

Two complex numbers x + iy = c + id ⇔ x = c and y = d

Real parts should be equal and Imaginary parts should be

equal,

So, on comparing real terms we get

a = 2 + b---------(1)

On comparing imaginary terms, we get

3 = b - 2

b = 5

Substituting b = 5 in 1, we get a = 2 + 5 = 7

Hence, a = 7 and b = 5

Consider 5a - 7b

= 5(7) - 7(5)

= 35 - 35

= 0

Hence 5a - 7b = 0

Hope, it helps !