Complex Analysis Answers

Let p(z,w)=α0(z)+α1(z)w+….+αk(z)wk ,where k≥1 and α0,…,αk are non-constant polynomials in the complex variable z. then {(z,w)∈C×C:p(z,w)=0} is
Bounded with empty interior.
Unbounded with empty interior.
bounded with nonempty interior .
bounded with nonempty interior.

Marion, Inc. has 5,000 shares of 5%, $100 par value, noncumulative preferred stock and 20,000 shares of $1 par value common stock outstanding at December 31, 2012. There were no dividends declared in 2011. The board of directors declares and pays a $55,000 dividend in 2012. What is the amount of dividends received by the common stockholders in 2012?
Answer A. $0
B. $25,000
C. $55,000
D. $30,000

The mean value theorem of a real-valued function of a real variable does not hold in general for complex-valued functions

A real-valued function u in domain D cannot be analytic in D unless it is a constant function.true/false

There exists a non-constant real-valued function u in open set D which is analytic in D.true/false

A real-valued function $u(x,y)$ is harmonic in D iff $u(x,-y)$ is harmonic in D

If f:$D→D’$ is analytic and u: $D'→R$ is harmonic then the composition of u & f is harmonic in D. true/false