Tamil Nadu Board of Secondary EducationHSC Arts Class 12

If z1 = 3, z2 = 7i, and z3 = 5 + 4i, show that (z1 + z2)z3 = z1z3 + z2z3 - Mathematics

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Sum

If z1 = 3, z2 = 7i, and z3 = 5 + 4i, show that (z1 + z2)z3 = z1z3 + z2z3

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Solution

z1 + z= 3 – 7i

(z1 + z2)z3 = (3 – 7i)(5 + 4i)

= 15 + 12i – 35i + 28i2

= 15 + 12i – 35i + 28i

= 43 – 23i  .......(1)

z1z3 = 3(5 + 4i) = 15 + 12i

z2z= – 7i(5 + 4i) = – 35i – 28i2

= – 35i + 28

z1z3 + z2z= (15 + 12i) + (– 35i + 28)

= 15 + 12i – 35i + 28

= 43 – 23i  .......(2)

∴ From 1 and 2

(z1 + z2)z3 = z1z3 + z2z3

Hence proved.

Concept: Basic Algebraic Properties of Complex Numbers
  Is there an error in this question or solution?
Chapter 2: Complex Numbers - Exercise 2.3 [Page 60]

APPEARS IN

Tamil Nadu Board Samacheer Kalvi Class 12th Mathematics Volume 1 and 2 Answers Guide
Chapter 2 Complex Numbers
Exercise 2.3 | Q 2. (ii) | Page 60
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