Q. 1 E4.2( 9 Votes )

Simplify each of the following and express it in the form a + ib :(1 – i)2 (1 + i) – (3 – 4i)2

Given: (1 – i)2 (1 + i) – (3 – 4i)2

= (1 + i2 – 2i)(1 + i) – (9 + 16i2 – 24i)

[(a – b)2 = a2 + b2 – 2ab]

= (1 – 1 – 2i)(1 + i) – (9 – 16 – 24i) [ i2 = -1]

= (-2i)(1 + i) – (- 7 – 24i)

Now, we open the brackets

-2i × 1 – 2i × i + 7 + 24i

= -2i – 2i2 + 7 + 24i

= -2(-1) + 7 + 22i [, i2 = -1]

= 2 + 7 + 22i

= 9 + 22i

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)

(iii) .

RS Aggarwal - Mathematics

RS Aggarwal - Mathematics

RS Aggarwal - Mathematics

If then show that

RD Sharma - Mathematics

RS Aggarwal - Mathematics

RS Aggarwal - Mathematics