Question

(a+ib) (1+I)=2+I .find a and b

Answer 1

Here's your solution!

Hope it's helpful

Answer 2

Answer:

a=$\frac{3}{2}$ and b= $\frac{-1}{2}$

Step-by-step explanation:

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

a + ai + bi + $bi^{2}$ = 2 + i

a + ai + bi +b(-1) = 2+ i

a + ai + bi - b = 2 + i

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

a - b = 2    and   a + b = 1

Simultaneously equate:

a + b = 1

a - b = 2

 2b = -1

 b = $\frac{-1}{2}$

To find a, just replace the value with the variable(b):

a + $\frac{-1}{2}$ = 1

a= $\frac{1}{2}$ + 1

a = $\frac{3}{2}$  or 1.5.