Q. 24

# Mark the Correct alternative in the following:

If x + i y = (1 + i) (1 + 2 i) (1 + 3i), then x^{2} + y^{2} =

A. 0

B. 1

C. 100

D. None of these

Answer :

Given that (1 + i) (1 + 2i) (1 + 3i) = x + i y …(1)

We can also say that

(1 - i) (1 - 2i) (1 - 3i) = x - i y …(2)

Multiply and divide the eq no. 2 with eq no. 1

((1)^{2} – (i)^{2})((1)^{2} – (2i)^{2})((1)^{2} – (3i)^{2}) = ((x)^{2} – (iy)^{2})

x^{2} + y^{2} = 2 × 5 × 10 = 100

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

Questions on Modulus & Conjugate of Complex Number62 mins

Special Quiz on Argument of complex numbers56 mins

Polar & Euler Form of Complex Number on Argand Plane58 mins

Questions Based on Polar & Euler Form of Complex Number63 mins

Get in the world of Complex Numbers55 mins

Discussion | Miscellaneous Exercise | NCERT Chapter 5| Complex Numbers47 mins

Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Expertsview all courses

Dedicated counsellor for each student

24X7 Doubt Resolution

Daily Report Card

Detailed Performance Evaluation

RELATED QUESTIONS :

Evaluate.

RS Aggarwal - MathematicsEvaluate

RS Aggarwal - Mathematics

If then show that

RD Sharma - MathematicsIf (1 + i)z = (1 – i) then prove that z = -

RS Aggarwal - Mathematics