Example 3 - Chapter 4 Class 11 Complex Numbers

Last updated at April 8, 2024 by

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Example 3 Express (5 – 3i)3 in the form a + ib. (5 – 3i)3 It is of the form (a – b)3 Using (a – b)3 = a3 - b3 – 3ab (a – b) Putting a = 5, b = 3i The above equation becomes (5 – 3 i)3 = 53 – (3i)3 – 3 × 5 × (3i) (5 – 3 i) = 125 – 27 i3 – 45i (5 – 3i) = 125 − 27 i × (i2) – 45 i × (5) + 45 i × (3 i) = 125 − 27 i (i2) – 225 i + 135(i2) = 125 − 27 i (−1) – 225 i + 135(–1) = 125 + 27 i – 225 i – 135 = 125 – 135 + i (27 – 225) = – 10 + i (–198) = – 10 – i 198

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.