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Last updated at Jan. 19, 2019 by Teachoo

Transcript

Ex 5.1, 10 Express the given Complex number in the form a + ib: (โ2โ1/3 ๐)^3 (โ2โ1/3 ๐)^3 = โ 1 (2+1/3 ๐)^3 = โ (2+1/3 ๐)^3 It is of the form (a + b)3 Using (a + b)3 = a3 + b3 + 3 ab (a + b) Here a = 2 and b = 1/3 i = โ((2)^3+(1/3 ๐)^3+3 ร2ร1/3 ๐(2+1/3 ๐)) = โ(8+(1/3)^3ร(๐)^3+2๐(2+1/3 ๐)) = โ(8+1/27 ๐^3+4๐+2/3 ๐^2 ) = โ(8+1/27 ใ๐ร๐ใ^2+4๐+2/3 ๐^2 ) Putting ๐^2=โ1 = โ1 (8+1/27 ๐(โ1)+4๐+2/3 (โ1)) = โ1 (8โ1/27 ๐+4๐โ2/3) = โ 8 + 1/27 ๐ โ 4i + 2/3 = โ 8 + 2/3 + ( 1)/27 ๐ โ 4๐ = (โ 8+ 2/3) + (( 1)/27โ4)๐ = ((โ24 + 2)/3) + ((1 โ 4 ร27)/27)๐ = (โ22)/3 + ((1 โ108)/27)๐ = (โ22)/3 + (( โ107)/27)๐ = (โ22)/3 โ ( 107)/27 ๐

Class 11

Important Questions for exams Class 11

- Chapter 1 Class 11 Sets
- Chapter 2 Class 11 Relations and Functions
- Chapter 3 Class 11 Trigonometric Functions
- Chapter 4 Class 11 Mathematical Induction
- Chapter 5 Class 11 Complex Numbers
- Chapter 6 Class 11 Linear Inequalities
- Chapter 7 Class 11 Permutations and Combinations
- Chapter 8 Class 11 Binomial Theorem
- Chapter 9 Class 11 Sequences and Series
- Chapter 10 Class 11 Straight Lines
- Chapter 11 Class 11 Conic Sections
- Chapter 12 Class 11 Introduction to Three Dimensional Geometry
- Chapter 13 Class 11 Limits and Derivatives
- Chapter 14 Class 11 Mathematical Reasoning
- Chapter 15 Class 11 Statistics
- Chapter 16 Class 11 Probability

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.