Q. 44.2( 9 Votes )

If (x + iy)1/3 = (a + ib) then prove that = 4 (a2 – b2).

Answer :

Given that, (x + iy)1/3 = (a + ib)


(x + iy) = (a + ib)3


(a + ib)3 = x + iy


a3 + (ib)3 + 3a2ib + 3ai2b2 = x + iy


a3 - ib3 + 3a2ib - 3ab2 = x + iy


a3 - 3ab2 + i(3a2b - b3) = x + iy


On equating real and imaginary parts, we get


x = a3 - 3ab2 and y = 3a2b - b3


Now ,



= a2 - 3b2 + 3a2 - b2


= 4a2 - 4b2


= 4(a2 - b2)


Hence,


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
Practice session | Argument of complex numbers61 mins
Modulus & Conjugate of Complex Number | Ready for a Quiz?48 mins
Interactive Quiz on Quadratic Equations73 mins
Special Quiz on Argument of complex numbers56 mins
Polar & Euler Form of Complex Number on Argand Plane58 mins
Questions on Modulus & Conjugate of Complex Number62 mins
Questions Based on Polar & Euler Form of Complex Number63 mins
Interactive Quiz on Quadratic Equations-0252 mins
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)


(ii)


(iii) .


RS Aggarwal - Mathematics

RS Aggarwal - Mathematics

RS Aggarwal - Mathematics

If then show that

RD Sharma - Mathematics

RS Aggarwal - Mathematics

RS Aggarwal - Mathematics