Question

(a+ib)(1+i)=2+i find a and b

Answer 1

Answer:

This is my explanation.

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Answer 2

Answer:

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

Step-by-step explanation:

Given : Expression $(a+ib)(1+i)=2+i$

To find : The value of a and b ?

Solution :

Solve the expression LHS,

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

$a+ai+ib-b=2+i$

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

Comparing LHS and RHS,

$a-b=2$....(1) and $a+b=1$ .....(2)

Solving these two equation by adding them,

$a-b+a+b=2+1$

$2a=3$

$a=\frac{3}{2}$

Substitute in equation (1),

$\frac{3}{2}-b=2$

$b=\frac{3}{2}-2$

$b=-\frac{1}{2}$

Therefore, The values are $a=\frac{3}{2}$ and $b=-\frac{1}{2}$