Class XI Chapter 5 – Complex Numbers and Quadratic Equations Maths ______________________________________________________________________________ 4i 2i 2 1i 1i 1i 1i 2 2i 2 2 Question 16: If 3 , x iy u iv Solution 16: 3 x iy u iv then show that: 3 3 3 x iy x iy x iy u iv 3 3 3 2 2 2 x i y 3x yi 3xy i u iv 3 3 2 2 x iy 3x yi 3xy u iv 3 2 2 3 x 3xy i 3x y y u iv u v 4 x y x y On equating real and imaginary parts, we obtain u x 3 xy , v 3x y y 3 2 2 3 u v x 3xy 3x y y x y x y 3 2 2 3 x x 3y y 3x y x y 2 2 2 2 x 3y 3x y 2 2 2 2 4x 4y 2 2 4 x y 2 2 u v 4 x y x y Hence, proved. 2 2 2 2

Class XI Chapter 5 – Complex Numbers and Quadratic Equations Maths ______________________________________________________________________________ Question 17: If and are different complex numbers with 1, then find 1 Solution 17: Let a ib and It is given that, 1 2 2 x y 1 x iy 2 2 x y 1 ....... i x iy a ib 1 1 a ib x iy x a i y b 1 ax aiy ibx by x a i y b 1 ax by i bx ay 1 x a i y b z 1 1 ax by i bx ay z2 z2 x a y b 2 2 1 ax by bx ay 2 2 z 2 2 2 2 x a 2ax y b 2by 2 2 2 2 2 2 2 2 1 2 2 2 2 a x b y ax abxy by b x a y abxy 2 2 2 2 x y a b 2ax 2by 2 2 2 2 2 2 1 2 2 a x y b y x ax by 2 2 1 a b 2ax 2by Using 1 2 2 1 a b 2ax 2by 1 1

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Class XI Chapter 12 - Introduction

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