Simplify. 9 i - ( i 2 ) 3

We have, 9 i - i 2 3 = 9 i - i · i 2 · 2 2 = 9 i - - 2 2 i = 9 i + 2 2 i = 9 + 2 2 i Hence, 9 i - i 2 3 = ( 9 + 2 2 ) i

Solve. x 2 + 64 25 = 0

Given, x 2 + 64 25 = 0 The given equation is of the form, a x 2 + b x + c = 0 , where a = 1 , b = 0 , and c = 64 25 Now, b 2 - 4 a c = 0 - 4 1 64 25 = - 256 25 < 0 So, the given equation has complex roots. These roots are given by x = - b ± b 2 - 4 a c 2 a = 0 ± - 256 25 2 1 = 0 ± i 256 25 2 ∵ i = - 1 = ± 16 5 i 2 = ± 8 5 i ∴ Solution Set = 8 5 i , - 8 5 i

Given, 4 x 2 + 7 = 0 The given equation is of the form, a x 2 + b x + c = 0 , where a = 4 , b = 0 , and c = 7 Now, b 2 - 4 a c = 0 - 4 4 7 = - 112 < 0 So, the given equation has complex roots. These roots are given by x = - b ± b 2 - 4 a c 2 a = 0 ± - 112 2 4 = 0 ± 4 7 i 8 ∵ i = - 1 = ± 7 i 2 ∴ Solution Set = 7 i 2 , - 7 i 2

E M B I B E

Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book>Chapter 11 - Complex Numbers>EXERCISE 11A

Sue Pemberton, Julianne Hughes and, Julian Gilbey Solutions for Chapter: Complex Numbers, Exercise 2: EXERCISE 11A

Author:Sue Pemberton, Julianne Hughes & Julian Gilbey

Sue Pemberton Mathematics Solutions for Exercise - Sue Pemberton, Julianne Hughes and, Julian Gilbey Solutions for Chapter: Complex Numbers, Exercise 2: EXERCISE 11A

Attempt the free practice questions on Chapter 11: Complex Numbers, Exercise 2: EXERCISE 11A with hints and solutions to strengthen your understanding. Cambridge International AS & A Level Mathematics : Pure Mathematics 2 & 3 Course Book solutions are prepared by Experienced Embibe Experts.