Question 6, Exercise 1.2

Solutions of Question 6 of Exercise 1.2 of Unit 01: Complex Numbers. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan.

Find the value of λ; if |z1z2+λ|=λ+2; where z1=3+i and z2=1+i.

Solution.

Given: z1=3+i and z2=1+i. Now z1z2=3+i1+i=(3+i)(1i)(1+i)(1i)=3+1+i(3+1)1+1=42i2=2i. Now |z1z2+λ|=λ+2|2i+λ|=λ+2|2+λi|2=λ+2(2+λ)2+1=λ+24+4λ+λ2+1λ2=0λ2+3λ+3=0. By using quadratic formula, we have λ=3±94(1)(3)2(1)=3±32=3±i32