Examples

Chapter 4 Class 11 Complex Numbers
Serial order wise

a

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

### Transcript

Example 7 Convert the given complex number in polar form: 1 + i√3. Given z = 1+ √3i Let polar form be z = r (cos⁡θ + i sin⁡θ) From ( 1 ) & ( 2 ) 1 + √3i = r ( cos⁡θ + i sin⁡θ) 1 + √3i = r〖 cos〗⁡θ + 𝑖 r sin⁡θ Adding (3) & (4) 1 + 3 = r2 cos2⁡θ + r2 sin2⁡θ 4 = 𝑟2 cos2⁡θ + r2 sin2⁡θ 4 = 𝑟2 ( cos2⁡θ + sin2⁡θ ) 4 = 𝑟2 × 1 4 = 𝑟2 √4 = 𝑟 r = 2 Hence, Modulus = 2 Finding argument 1 + √3i = r〖 cos〗⁡θ + 𝑖 r sin⁡θ Comparing real part 1 = r cos⁡θ Putting r = 2 1 = 2cos⁡θ 1/2 = cos⁡θ cos⁡θ = 1/2 Hence, sin⁡θ = √3/2 & cos θ = 1/2 Hence, sin⁡θ = √3/2 & cos θ = 1/2 Since sin θ and cos θ both are positive, Argument will be in Ist quadrant Argument = 60° = 60 × 𝜋/180 = 𝜋/3 Hence θ = 𝜋/3 and r = 2 Polar form of z = r ( cos θ + 𝑖 sin θ ) = 2 ( cos 𝜋/3 + 𝑖 sin 𝜋/3)

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#### Davneet Singh

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.