Complex Numbers 2 Question 44
45. Find the real values of $x$ and $y$ for which the following equation is satisfied
$$ \frac{(1+i) x-2 i}{3+i}+\frac{(2-3 i) y+i}{3-i}=i \text {. } $$
$(1980,2 M)$
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Solution:
- $\frac{(1+i) x-2 i}{3+i}+\frac{(2-3 i) y+i}{3-i}=i$
$\Rightarrow(1+i)(3-i) x-2 i(3-i)+(3+i)(2-3 i) y$
$$ +i(3+i)=10 i $$
$\Rightarrow \quad 4 x+2 i x-6 i-2+9 y-7 i y+3 i-1=10 i$
$\Rightarrow \quad 4 x+9 y-3=0$ and $2 x-7 y-3=10$
$$ \Rightarrow \quad x=3 \text { and } y=-1 $$
