Example 3 - Express (5 - 3i)3 in a + ib - Class 11 NCERT - Identities (square, cube of 2 complex numbers)

Example 3 - Chapter 5 Class 11 Complex Numbers - Part 2

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Transcript

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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.