Complex Analysis

Front

Back

The function is differentiable only at z=0.

Front

Back

The function is constant.

Front

What is the statement regarding a non-constant entire function in terms of complex values?

Back

A non-constant entire function assumes each complex value, with one possible exception.

Front

What is the sum of the orders of the zeros of a polynomial of degree n?

Back

The sum is equal to n.

Front

Back

20 is not a possible value.

Front

Define an entire function.

Back

An entire function is a complex function that is holomorphic (differentiable) at all points in the complex plane.

Front

What is the Cauchy-Riemann equation?

Back

The Cauchy-Riemann equations are a set of two equations that must be satisfied for a function to be holomorphic.

Front

What is the significance of the maximum modulus principle in complex analysis?

Back

The maximum modulus principle states that if a function is holomorphic in a domain, then its maximum modulus occurs on the boundary of the domain.

Front

What is a zero of a complex function?

Back

A zero of a complex function is a point in the complex plane where the function evaluates to zero.

Front

What is Liouville's theorem?

Back

Liouville's theorem states that any bounded entire function must be constant.