Modulus, Argument, Polar Representation

Chapter 4 Class 11 Complex Numbers
Serial order wise

### Transcript

Question 4 Convert the given complex number in polar form: โ 1 + i Given ๐ง = โ1+ ๐ Let polar form be ใ๐ง = ๐ (cosใโกฮธ+๐ sinโกฮธ) From (1) & (2) โ 1+ ๐ = r ( cosโกฮธ + ๐ sinโกฮธ) โ 1+ ๐ = rใ cosใโกฮธ + ๐ r sinโกฮธ Adding ( 3 ) and ( 4 ) 1 + 1 = ๐2 cos2 ฮธ+ ๐2 sin2ฮธ 2 = ๐2 ( cos2 ฮธ+ sin2 ฮธ) 2 = ๐2 ร 1 2 = ๐2 โ2 = ๐ ๐ = โ2 Finding argument โ 1+ ๐ = rใ cosใโกฮธ + ๐ r sinโกฮธ Hence, sin ฮธ = 1/โ2 & cos ฮธ = (โ 1)/โ2 Hence, sin ฮธ = 1/โ2 & cos ฮธ = (โ 1)/โ2 Here, sin ฮธ is positive and cos ฮธ is negative, Hence, ฮธ lies in IInd quadrant Argument = 180ยฐ โ 45ยฐ = 135ยฐ = 135ยฐ ร ๐/180o = ( 3 ๐)/4 So argument of z = ( 3 ๐)/4 Hence ๐ = โ2 and ฮธ = 3๐/4 Polar form of z = r (cos ฮธ + sin ฮธ) = โ2 (cos (( 3 ๐)/4)+ ๐ sin(( 3 ๐)/4))

#### Davneet Singh

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.