Last updated at May 29, 2018 by Teachoo
Transcript
Example 7 Convert the given complex number in polar form: 1 + i√3. Given z = 1+ √3i Let polar form be z = r (cosθ + i sinθ) From ( 1 ) & ( 2 ) 1 + √3i = r ( cosθ + i sinθ) 1 + √3i = r〖 cos〗θ + 𝑖 r sinθ Adding (3) & (4) 1 + 3 = r2 cos2θ + r2 sin2θ 4 = 𝑟2 cos2θ + r2 sin2θ 4 = 𝑟2 ( cos2θ + sin2θ ) 4 = 𝑟2 × 1 4 = 𝑟2 √4 = 𝑟 r = 2 Hence, Modulus = 2 Finding argument 1 + √3i = r〖 cos〗θ + 𝑖 r sinθ Comparing real part 1 = r cosθ Putting r = 2 1 = 2cosθ 1/2 = cosθ cosθ = 1/2 Hence, sinθ = √3/2 & cos θ = 1/2 Hence, sinθ = √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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Example 2 (i)
Example 2 (ii) Important
Example 3
Example 4
Example 5 Important
Example 6 (i)
Example 6 (ii) Important
Example 7 Deleted for CBSE Board 2022 Exams You are here
Example 8 Important Deleted for CBSE Board 2022 Exams
Example 9
Example 10
Example 11 Important
Example 12
Example 13 (i) Important Deleted for CBSE Board 2022 Exams
Example 13 (ii) Deleted for CBSE Board 2022 Exams
Example 14 Important
Example 15
Example 16 Important Deleted for CBSE Board 2022 Exams
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