Class XI Chapter 5 – Complex Numbers and Quadratic Equations Maths ______________________________________________________________________________ 1 2 z 2 1 1 1z2 1 i i z z 1 2 i 1 i 1 4 4 2 2i 2 1i 2 1 i 21 i 2 2 1i 1i 1 i i 2 21 **11** 21 i 2 2 2 1 i 1 1 2 i 1 Thus, the value of z z z z 1 2 1 2 1 1 is 2 . Question **11**: If a ib x i 2 2 2x 1 Solution **11**: a ib x i 2 2 2x 1 2 2 x i 2xi 2 2x 1 x 2 1i2x 2 2x 1 , prove that a b 2 2 x 2 1 2x 1 2 x 1 2x i 2 2 2x 1 2x 1 On comparing real and imaginary parts, we obtain a x 2 1 and 2x b 2 2x 1 2 2x 1 2 2

Class XI Chapter 5 – Complex Numbers and Quadratic Equations Maths ______________________________________________________________________________ 2 2 2 2 2 x 1 2x a b 2 2 x 1 2x 4x 2 2x 1 x 2x 1 2x 1 4 2 2 12x 4 2 2 2 2x 1 x 2 1 2 2 2 2x 1 2 2 a b x Hence, proved. 2 1 2 2 2 2x 1 Question 12: Let z 2 i, z 2 i 1 2 Solution 12: z 2 i, z 2 i (i) z 1 2 . Find zz 1 ( ii) Im zz 1 2 ( i) Re , z1 1 1 2 z1z2 2 i 2 i 4 2i 2i i 4 4i 1 3 4i 1 2 z z z 1 2 1 i 34i 2 i 2 i On multiplying numerator and denominator by 2 z1z i i 2 6 3i 8i 4i i z i i 1 3 4 2 6 **11** 4 1 2 2 2 1 2 1 2 **11**i 2 **11** i 5 5 5 On comparing real parts, we obtain zz 1 2 2 Re z 5 1 (ii) 1 1 1 1 zz 1 1 i i 2 1 2 2 2 2 5 2 2 2 2 , we obtain

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Class XI Chapter 12 - Introduction

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Class XI Chapter 13 - Limits and De

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Class XI Chapter 15 - Statistics Ma

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