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The function f(z) of complex variable z = x + iy, where i = √−1, is given as f(z) = (x3 – 3xy2) + i v(x,y). For this function to be analytic, v(x,y) should be
  • a)
    (3xy2 – y3) + constant
  • b)
    (3x2y2 – y3) + constant
  • c)
    (x3 – 3x2y) + constant
  • d)
    (3x2y – y3) + constant
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The function f(z) of complex variable z = x + iy, where i = √&mi...
Concept:
f(z) = u + iv
u = real part
v = imaginary part
If f(z) is an analytic function

(This is an exact differential equation)
Calculation:
Given,
u = x3 – 3xy2
∂u/∂x = 3x2 − 3y2
∂u/∂y = −6xy

It is an exact differential equation the solution is obtained by treating y as constant in the first term and in the second term only that part is integrated which is not containing x.
Integrating the above equation
v = 3x2y − y+ constant
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The function f(z) of complex variable z = x + iy, where i = √−1, is given as f(z) = (x3 – 3xy2) + i v(x,y). For this function to be analytic, v(x,y) should bea)(3xy2 – y3) + constantb)(3x2y2 – y3) + constantc)(x3 – 3x2y) + constantd)(3x2y – y3) + constantCorrect answer is option 'D'. Can you explain this answer?
Question Description
The function f(z) of complex variable z = x + iy, where i = √−1, is given as f(z) = (x3 – 3xy2) + i v(x,y). For this function to be analytic, v(x,y) should bea)(3xy2 – y3) + constantb)(3x2y2 – y3) + constantc)(x3 – 3x2y) + constantd)(3x2y – y3) + constantCorrect answer is option 'D'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about The function f(z) of complex variable z = x + iy, where i = √−1, is given as f(z) = (x3 – 3xy2) + i v(x,y). For this function to be analytic, v(x,y) should bea)(3xy2 – y3) + constantb)(3x2y2 – y3) + constantc)(x3 – 3x2y) + constantd)(3x2y – y3) + constantCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The function f(z) of complex variable z = x + iy, where i = √−1, is given as f(z) = (x3 – 3xy2) + i v(x,y). For this function to be analytic, v(x,y) should bea)(3xy2 – y3) + constantb)(3x2y2 – y3) + constantc)(x3 – 3x2y) + constantd)(3x2y – y3) + constantCorrect answer is option 'D'. Can you explain this answer?.
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