Q. 21 D4.8( 5 Votes )

# Find the real values of x and y for which:(1 + i) y2 + (6 + i) = (2 + i)x

Given: (1 + i) y2 + (6 + i) = (2 + i)x

Consider, (1 + i) y2 + (6 + i) = (2 + i)x

y2 + iy2 + 6 + i = 2x + ix

(y2 + 6) + i(y2 + 1) = 2x + ix

Comparing the real parts, we get

y2 + 6 = 2x

2x – y2 – 6 = 0 …(i)

Comparing the imaginary parts, we get

y2 + 1 = x

x – y2 – 1 = 0 …(ii)

Subtracting the eq. (ii) from (i), we get

2x – y2 – 6 – (x – y2 – 1) = 0

2x – y2 – 6 – x + y2 + 1 = 0

x – 5 = 0

x = 5

Putting the value of x = 5 in eq. (i), we get

2(5) – y2 – 6 = 0

10 – y2 – 6 = 0

-y2 + 4 = 0

- y2 = -4

y2 = 4

y = √4

y = ± 2

Hence, the value of x = 5 and y = ± 2

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Polar & Euler Form of Complex Numbers on Argand Plane32 mins
Interactive Quiz Time - Polar & Euler Form of complex number58 mins
Interactive Quiz on Quadratic EquationsFREE Class
Modulus & Conjugate of Complex Number | Ready for a Quiz?48 mins
Practice session | Argument of complex numbersFREE Class
Special Quiz on Argument of complex numbersFREE Class
Polar & Euler Form of Complex Number on Argand Plane58 mins
Questions Based on Polar & Euler Form of Complex Number63 mins
Questions on Modulus & Conjugate of Complex Number62 mins
Interactive Quiz on Quadratic Equations-02FREE Class
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :

Evaluate.

RS Aggarwal - Mathematics

Evaluate

RS Aggarwal - Mathematics

Evaluate:

(i)

(iii) .

RS Aggarwal - Mathematics

RS Aggarwal - Mathematics

RS Aggarwal - Mathematics

If then show that

RD Sharma - Mathematics

RS Aggarwal - Mathematics