Class XI Chapter 5 – Complex Numbers and Quadratic Equations Maths ______________________________________________________________________________ Question 4: Convert the given complex number in polar form: Solution 4: 1 i Let and On squaring and adding, we obtain r r cos 1 rsin 1 2 cos r sin 1 1 2 2 2 2 2 2 2 2 r r 2 cos sin 1 1 2 1i r 2 [Conventionally, r > 0] 2 cos 1 cos 1 2 and and 2 sin 1 2 sin 1 3 [As lies in the II quadrant] 4 4 It can be written, 3 3 3 3 1 i r cos i r sin 2 cos i 2 sin 2 cos isin 4 4 4 4 This is the required polar form. Question 5: Convert the given complex number in polar form: Solution 5: 1i r cos 1 r sin 1 Let and On squaring and adding, we obtain r 2 2 2 2 2 2 cos r sin 1 1 2 2 2 r 2 r r cos sin 1 1 2 2 2 cos 1 and 2 sin 1 1 1 cos and sin 2 2 1i [Conventionally, r 0 ]

Class XI Chapter 5 – Complex Numbers and Quadratic Equations Maths ______________________________________________________________________________ 3 4 4 [As lies in the III quadrant] 3 3 3 3 1 i r cos i r sin 2 cos i 2 sin 2 cos isin 4 4 4 4 This is the required polar form. Question 6: Convert the given complex number in polar form: Solution 6: 3 r cos 3 r sin 0 Let and On squaring and adding, we obtain r 2 2 2 2 2 cos r sin 3 2 2 2 r r 2 cos sin 9 9 r 9 3 [Conventionally, r > 0] and 3sin 0 3cos 3 cos 1 and sin 0 3 r cos i r sin 3cos i3sin 3 cos isin This is the required polar form. 3 Question 7: Convert the given complex number in polar form: 3 i Solution 7: 3 i Let and rsin 1 On squaring and adding, we obtain r r cos 3 2 cos r sin 3 1 2 2 2 2 2 2 2 2 r cos sin 3 1

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Class XI Chapter 12 - Introduction

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Class XI Chapter 13 - Limits and De

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