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Class XI Chapter 5 – Complex Numbers and Quadratic Equations Maths ______________________________________________________________________________ r 2 4 r 4 2 Conventionally, r 0 2cos 3 cos 6 3 2 and 2sin 1 1 and sin 2 [As lies in the I quadrant] 3 i r cos i r sin 2cos i 2sin 2cos isin 6 6 6 6 This is the required polar form. Question 8: Convert the given complex number in polar form: i Solution 8: i Let rcos 0 and rsin 1 On squaring and adding, we obtain r cos r sin 0 1 2 2 2 2 2 2 2 2 2 r r 2 cos sin 1 1 r 1 1 Conventionally, r 0 cos 0 and sin 1 2 i r cos i r sin cos i sin 2 2 This is the required polar form.
Class XI Chapter 5 – Complex Numbers and Quadratic Equations Maths ______________________________________________________________________________ Exercise 5.3 Question 1: Solve the equation Solution 1: 2 x 30 The given quadratic equation is 2 x On comparing the given equation with We obtain a 1, b 0, and c 3 3 0 2 ax bx c 0, Therefore, the discriminant of the given equation is 2 2 D b 4ac 0 413 12 Therefore, the required solutions are b D 12 12i 1 i 2a 21 2 2 3i 2 3i Question 2: Solve the equation Solution 2: 2 2x x1 0 The given quadratic equation is On comparing the given equation with We obtain and a2, b1 c 1 2 2x x1 0 2 ax bx c 0 Therefore, the discriminant of the given equation is 2 2 D b 4ac 1 4 21 18 7 Therefore, the required solutions are b D 1 7 1 7i 1 i 2a 2 2 4 , Question 3: Solve the equation Solution 3: x 2 3x 9 0 2 The given quadratic equation is x 3x 9 0
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Class XI Chapter 1 - Sets Maths ___
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Class XI Chapter 2 - Relations and
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Class XI Chapter 3 - Trigonometric
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Class XI Chapter 6 - Linear Inequal
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Class XI Chapter 7 - Permutation an
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Class XI Chapter 8 - Binomial Theor
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Class XI Chapter 9 - Sequences and
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Class XI Chapter 10 - Straight Line
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Class XI Chapter 11 - Conic Section
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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 14 - Mathematical
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Class XI Chapter 15 - Statistics Ma
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