Question

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

Answer 1

Answer:

Solution is in attachment.

Answer 2

$Answer:</p><p></p><p>The \: values \: are </p><p>\: a=\frac{3}{2}a=23 and b=-\frac{1}{2}b=−21</p><p> </p><p>Step - by- step \: explanation:</p><p></p><p>Given : Expression (a+ib)(1+i)=2+i(a+ib)(1+i)=2+i</p><p></p><p>To find : The value of a and b ?</p><p></p><p>Solution :</p><p></p><p>Solve the expression LHS,</p><p></p><p>a(1+i)+ib(1+i)=2+ia(1+i)+ib(1+i)=2+i</p><p></p><p>a+ai+ib-b=2+ia+ai+ib−b=2+i</p><p></p><p>(a-b)+i(a+b)=2+i(a−b)+i(a+b)=2+i</p><p></p><p>Comparing LHS and RHS,</p><p></p><p>a-b=2a−b=2 ....(1) and a+b=1a+b=1 .....(2)</p><p></p><p>Solving these two equation by adding them,</p><p></p><p>a-b+a+b=2+1a−b+a+b=2+1</p><p></p><p>2a=32a=3</p><p></p><p>a=\frac{3}{2}a=23</p><p></p><p>Substitute in equation (1),</p><p></p><p>\frac{3}{2}-b=223−b=2</p><p></p><p>b=\frac{3}{2}-2b=23−2</p><p></p><p>b=-\frac{1}{2}b=−21</p><p></p><p>Therefore, The values are a=\frac{3}{2}a=23 and b=-\frac{1}{2}b=−21</p><p></p><p>$