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Given two complex numbers Z1 = 5 + (5√3)i, and Z2 = 2/√3 + 2i the argument of Z1/Z2 in degrees is
  • a)
    0
  • b)
    30
  • c)
    60
  • d)
    90
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Given two complex numbersZ1 = 5 + (5√3)i, andZ2 = 2/√3 + 2...
The argument of a complex number z = x + iy
arg⁡ z = tan−1 (y/x)
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Given two complex numbersZ1 = 5 + (5√3)i, andZ2 = 2/√3 + 2...
Given Complex Numbers:
Z1 = 5 + (5√3)i
Z2 = 2/√3 + 2i

Calculating Z1/Z2:
To find the argument of Z1/Z2, we first need to calculate the quotient Z1/Z2.
Z1/Z2 = (5 + (5√3)i) / (2/√3 + 2i)
= [(5 + (5√3)i) * (√3 - i)] / [(2/√3 + 2i) * (√3 - i)]
= [(5√3 + 5i) - 5√3 - 5] / (2 + 2√3i + 2√3 - 2i)
= (5i - 5) / (2 + 2√3i + 2√3 - 2i)
= (5i - 5) / (2√3 - 2 + 2√3i + 2i)
= [5(i - 1)] / [2(√3 - 1) + 2(i + √3)]
= [5(i - 1)] / [2(i + √3) + 2(√3 - 1)i]
= [5(i - 1)] / [2i + 2√3 + 2√3i - 2]
= [5(i - 1)] / [-2 + 2√3 + 2√3i + 2i]
= [5(i - 1)] / [-2 + 2√3(1 + i)]

Calculating Argument:
To find the argument of Z1/Z2, we need to find the angle that the complex number makes with the positive real axis in the complex plane.
Since the real part of Z1/Z2 is 0, the argument is 0 degrees.
Therefore, the correct answer is option 'A' (0).
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Given two complex numbersZ1 = 5 + (5√3)i, andZ2 = 2/√3 + 2i the argument ofZ1/Z2 in degrees isa)0b)30c)60d)90Correct answer is option 'A'. Can you explain this answer?
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