સમીકરણ frac{{(1 + i)x - 2i}}{{3 + i}} + frac{{(2 - 3i),y + i}}{{3

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4-1.Complex numbers

easy

સમીકરણ $\frac{{(1 + i)x - 2i}}{{3 + i}}$ $ + \frac{{(2 - 3i)\,y + i}}{{3 - i}} = i$ નું સમાધાન કરે તેવી $x$ અને $y$ ની કિમત મેળવો.

$x = - 1,\,y = 3$

$x = 3,\,y = - 1$

$x = 0,\,y = 1$

$x = 1,y = 0$

(IIT-1980)

Solution

(b) $\frac{{(1 + i)x – 2i}}{{3 + i}} + \frac{{(2 – 3i)y + i}}{{3 – i}} = i$
==> $(4 + 2i)x + (9 – 7i)y – 3i – 3 = 10i$
Equating real and imaginary parts, we get $2x – 7y = 13$ and $4x + 9y = 3$. Hence $x = 3$and $y = – 1$.
Trick : After finding the equations, no need to solve them, put the values of $x$ and $y$ given in the options and get the appropriate option.

Standard 11

Mathematics