Express 2+6√3i/5+√3i in polar form
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Answered by
42
Answer:
2 {cos(π/3) + i sin(π/3)}
Solution:
Let, z = (2 + 6√3i) / (5 + √3i)
= {(2 + 6√3i) (5 - √3i)}/{(5 + √3i) (5 - √3i)}
= (10 - 2√3i + 30√3i - 18i²)/(25 - 3i²)
= (10 + 28√3i + 18) / (25 + 3),
where i = √(- 1)
= (28 + 28√3i)/28
= 1 + i√3
Let, 1 + i√3 = r (cosθ + sinθ)
Then r cosθ = 1 and r sinθ = √3
Now, r² cos²θ + r² sin²θ = 4
Then r² = 4
So, r = 2
Then cosθ = 1/2 and sinθ = √3/2
This gives θ = π/3
Therefore mod z = 2 and arg z = π/3
Hence 1 + i√3 = 2 {cos(π/3) + i sin(π/3)}
Answered by
12
Answer:
see the answer is present in target publication guide part 2
Step-by-step explanation:
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