Project ForgeEngineering Mathematics
Calculus
GATE 2020
Medium
An analytic function of a complex variable z=x+iy (i=√−1) is defined as f(z) = x²−y² + iψ(x,y), where ψ(x,y) is a real function. The value of the imaginary part of f(z) at z=(1+i) is __________ (round off to 2 decimal places).
2(± 0.02 accepted)
Explanation
The real part x²−y² is the real part of z²=(x+iy)²=(x²−y²)+i(2xy), so by the Cauchy-Riemann equations f(z)=z² and ψ(x,y)=2xy. At z=1+i (x=1,y=1): ψ=2×1×1=2.
Source: GATE ME 2020 Session 1 (ME-1) (2020)
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