Answer :

Let, (a + ib)2 = -7 + 24i


Now using, (a + b)2 = a2 + b2 + 2ab


a2 + (bi)2 + 2abi = -7 + 24i


Since i2 = -1


a2 - b2 + 2abi = -7 + 24i


Now, separating real and complex parts, we get


a2 - b2 = -7…………..eq.1


2ab = 24…….. eq.2


a =


Now, using the value of a in eq.1, we get


– b2 = -7


144 – b4 = -7b2


4 - 7b2 - 144= 0


Simplify and get the value of b2 , we get,


b2 = -9 or b2 = 16


As b is real no. so, b2 = 16


b= 4 or b= -4


Therefore, a= 3 or a= -3


Hence the square root of the complex no. is 3 + 4i and -3 -4i.


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
Questions Based on Polar & Euler Form of Complex Number63 mins
Special Quiz on Argument of complex numbersFREE Class
Polar & Euler Form of Complex Number on Argand Plane58 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)


(ii)


(iii) .


RS Aggarwal - Mathematics

RS Aggarwal - Mathematics

RS Aggarwal - Mathematics

If then show that

RD Sharma - Mathematics

RS Aggarwal - Mathematics