Class XI Chapter 5 – Complex Numbers and Quadratic Equations Maths ______________________________________________________________________________ 3 2 1 i 3i 3i 1 i 3i 3 2 2i 22i Question 2: For any two complex numbers Re z 1 z z Re z Re z Im z Im z 1 2 1 2 1 2 Solution 2: Let z x iy 1 1 1 and z x iy 2 2 2 z z x iy x iy 1 2 1 1 2 2 x x iy iy x iy 1 2 2 1 2 2 x x ix y iy x i y y 2 1 2 1 2 1 2 1 2 and z 2 , prove that 2 x1x 2 ix1 y2 iy1x2 y1 y 2 i 1 x x y y i x y y x 1 2 1 2 1 2 1 2 Re z z x x y y 1 2 1 2 1 2 Re z z Re z Re z Im z Im z Hence, proved. 1 2 1 2 1 2 Question 3: Reduce Solution 3: 1 2 3 4i 1 4i 1 i 5 i 1 i 21 4i 1 2 34i 34i 1 4i 1 i 5 i 1 4i 1 i 5 i 1 i 2 8i 3 4i 1 9i 3 4i 2 1 i 4i 4i 5 i 5 3i 5 i 2 3 4i 27i 36i 33 31i 33 31i 2 25 5i 15i 3i 28 10i 2 14 5i

Class XI Chapter 5 – Complex Numbers and Quadratic Equations Maths ______________________________________________________________________________ 3331i 14 5i 2 14 5i 14 5i 2 462 165 434 155 307 599 i i i i 2 14 5 2 2 2 i 2196 25i 307 599i 307 599i 307 599i 2 221 442 442 442 This is the required standard form. 14 5i [On multiplying numerator and denominator by ] Question 4: If x iy Solution 4: x iy a ib c id a ib c id a ib c id c id c id ac bd i ad bc 2 c x iy d 2 2 2 2 x y 2ixy prove that x y 2 2 ac bd i ad bc c d 2 2 a c b d 2 2 2 2 [On multiplying numerator and denominator by c id ] ac bd iad bc 2 2 c d On comparing real and imaginary parts, we obtain ac bd ad bc , 2 ...... 1 c d c d 2 2 x y xy 2 2 2 2 2 2 x y x y 4x y 2 2 2 2 2 2 2 ac bd ad bc 2 2 2 2 c d c d 2 2 2 2 2 2 2 2 a c b d 2acbd a d b c 2adbc c d 2 2 2 [Using (1)]

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Class XI Chapter 12 - Introduction

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