Complex variables Topics - GATE ME Syllabus

1

Functions satisfying Cauchy-Riemann and being differentiable in complex plane.

1m4/10

📌 Key Formulaf(z) = u + iv

2

Necessary conditions for differentiability in complex domain.

1m3/10

📌 Key Formulaux = vy, uy = -vx

3

Integral of analytic function over closed contour is zero.

1m4/10

📌 Key Formula∮ f(z) dz = 0

4

Cauchy's integral formula for derivatives.

1m4/10

📌 Key Formulaf(a) = (1/2πi) ∮ f(z)/(z-a) dz

5

Power series expansion in complex plane.

1m4/10

📌 Key FormulaΣ [f^{(n)}(a)/n!] (z-a)^n

6

Expansion with negative powers for annular regions.

1m5/10

📌 Key FormulaΣ a_n (z-a)^n from -∞ to ∞