Electrical Engineering (EE) Exam > Electrical Engineering (EE) Questions > If v = 2xy, the analytic function f (z) = u ...
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If v = 2xy, the analytic function f (z) = u + iv is
- a)z2 + c
- b)z−2 + c
- c)z3 + c
- d)z−3 + c
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
If v = 2xy, the analytic function f (z) = u + iv isa)z2 + cb)z−2 + cc...
Given Information:
The given function is f(z) = u + iv, where v = 2xy.
Explanation:
Conversion to Complex Form:
We know that z = x + iy, where x and y are real numbers. Therefore, we can write z = x + iy = z + iz. Substituting this in the given function:
v = 2xy = 2i(x^2 - y^2) = 2i(z^2 - i^2z^2) = 2i(z^2 + z^2) = 4iz^2
Conclusion:
Comparing the given function with the converted form, we get f(z) = u + iv = z^2 + c, with c = 0. Therefore, the correct option is z^2 + c, which is option 'A'.
The given function is f(z) = u + iv, where v = 2xy.
Explanation:
Conversion to Complex Form:
We know that z = x + iy, where x and y are real numbers. Therefore, we can write z = x + iy = z + iz. Substituting this in the given function:
v = 2xy = 2i(x^2 - y^2) = 2i(z^2 - i^2z^2) = 2i(z^2 + z^2) = 4iz^2
Conclusion:
Comparing the given function with the converted form, we get f(z) = u + iv = z^2 + c, with c = 0. Therefore, the correct option is z^2 + c, which is option 'A'.
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Community Answer
If v = 2xy, the analytic function f (z) = u + iv isa)z2 + cb)z−2 + cc...
by Milne’s Method f’(z) = g(z,0) + ih(z,0) = 2z + i0 = 2z
On integrating f(z) = z2 + c
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If v = 2xy, the analytic function f (z) = u + iv isa)z2 + cb)z−2 + cc)z3 + cd)z−3 + cCorrect answer is option 'A'. Can you explain this answer?
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