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Q. If $(1-i) x+(1+i) y=1-3 i$, then $(x, y)=$

Complex Numbers and Quadratic Equations

Solution:

$(1-i) x+(1+i) y=1-3 i$
comparing the real and imaginary part
$ x+y=1 .....$(1)
$ -x+y=-3 .....$(2)
$ \Rightarrow x=2, y=-1$