Ex 5.2, 7 - Convert root 3 + i in polar form - Chapter 5 CBSE - Polar representation

Ex 5.2, 7 - Chapter 5 Class 11 Complex Numbers - Part 2
Ex 5.2, 7 - Chapter 5 Class 11 Complex Numbers - Part 3
Ex 5.2, 7 - Chapter 5 Class 11 Complex Numbers - Part 4

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Question 7 Convert the given complex number in polar form: 3 + i. Given z = 3 + i Let polar form be z = r (cos + i sin ) From (1) & (2) 3 + i = r (cos + i sin ) 3 + = r cos + r sin Adding (3) & (4) 3 + 1 = r2 cos2 + r2 sin2 4 = 2 cos2 + r2 sin2 4 = 2 ( cos2 + sin2 ) 4 = 2 1 4 = 2 4 = r = 2 Hence, Modulus = 2 Finding argument 3 + = r cos + r sin Comparing real part 3 = r cos Putting r = 2 3 = 2cos 3/2 = cos cos = 3/2 Hence, sin = 1/2 & cos = 3/2 Hence, sin = 1/2 & cos = 3/2 Since sin and cos both are positive, Argument will be in Ist quadrant Argument = 30 = 30 /180 = /6 Hence = /6 and r = 2 Polar form of z = r ( cos + sin ) = 2 ( cos /6 + sin /6)

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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.