Question

complex variables

sinply state Rouches theorem and use it in an example.

Answer #1

State the Fundamental Subspace Theorem and give an example of
its application in the case of a 2×2 matrix.

Complex Variables:
(a) Describe all complex numbers 'z' such that e^z = 1.
(b) Let 'w' be a complex number. Let 'a' be a complex number
such that e^a = w. Describe all complex numbers 'z' such that e^z =
w.

Use Demoivre's Theorem to find (2 + 5i) to the 3rd power. Use
degrees mode in your calculator. Write the answer in standard form
of a complex number, a + bi, and round numbers to the whole
number.

1. The following theorem can be proved by induction. State the
proposition form you’d use to prove the statement and complete the
base case.
Theorem: Suppose s : N → N be a function such that s(0) = 0 and s(n
+ 1) = s(n) + 1/[(n+1)(n+2)]. Then, s(n) =n/n+1

Complex Analysis:
Use Rouche's Theorem and Argument Principle to determine the
number of roots of p(z)=z^4-2z^3+13z^2-2z+36 which lie in each
quadrant of the plane.
(Hint: Consider |z|=5 and |z|=1)

explain what is superposition theorem in simple terms and give
an example and a step by step solution on how to use it

4. State and prove the Taylor’s Theorem.

Explain the tax benefit rule and use state income tax as an
example.

State the Fundamental Theorem of Calculus. Why is it such a big
deal?

In your own words, explain the remainder theorem and give an
example of how it is used. How is the factor theorem related to the
remainder theorem? What is synthetic division? Demonstrate how
synthetic division is used to find zeros of a polynomial.

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