Question

If 2x+ i (x - y) = 5, where x and y are real numbers, find the values of x and y
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Answer 1

Answer:

Given:Conjugate of −3+ix

2

y=x

2

+y−4i

Comparing real and imaginary parts, we get

x

2

+y=−3

x

2

y=−4

⇒x

2

=

y

−4

⇒x

2

+y=−3

⇒

y

−4

+y=−3

⇒y

2

+3y−4=0

⇒y

2

+4y−y−4=0

⇒y(y+4)−1(y+4)=0

⇒(y+4)(y−1)=0

⇒y=−4,1

⇒x

2

=

−4

−4

=1,x

2

=

1

−4

=−4

⇒x=±1,x=±2i

x=±2i is impossible since x is real.

∴x=±1,y=−4