# 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:

(i) (iii) .

RS Aggarwal - Mathematics