Question

If $x$ and $y$ are complex numbers, then system of equations $(1+i)x+(1-i)y=1,2ix+2y=1+i$ has

• A. unique solution
• B. no solution
• C. infinite numbers of solution
• D. none of these

Answer 1

Answer: (C)

infinite numbers of solution

$(1+i)x+(1-i)y=1$ ...(1)
$2ix+2y=1+i$ ...(2)
Multiply equation (2) with $\left(\frac{1-i}{2}\right)$ we get,
$i(1-i)x+(1-i)y=\frac{(1-i)(1+i)}{2}$
$⟹(i+1)x+(1-i)y=1$ ...(3)
Since eq. (1) & eq. (3) are similar.
Therefore, the system of equations have infinite solutions.
Hence, option 'C' is correct.