1. For each of the functions below, describe the domain of definition, and write each function in the form f(z) = u(x,y) +iv(x,y)
1) f(z) = z^2 / (z+z)
2) f(z) = z^3
3) f(z) = |z| + z
2. Suppose that f(z) = x^2 - y^2 - 2y + i(2x-2xy), where z = x +iy. Use the expressions
x = z+z / 2 and y = z-z /2i
to write f(z) in terms of z, and simplify the result.
3. Sketch the following sets and determine which are domains. If the set is NOT a domain, briefly explain why not.
[see the attachment for the full problem]
4. Evaluate the following limit. Show steps. If the limit does not exist, explain why not.
5. Let [see the attachment for the full equation]
Determine the value w so that the function f is continuous at z=0
6. Let f(x_iy) = e^x (cos y + i sin y) for all x, y, R. Prove that f is continuous on the complex plain.© BrainMass Inc. brainmass.com October 25, 2018, 8:00 am ad1c9bdddf
Step-by-step solutions that find the domain, limit and continuity of complex variables.
Contribution and Absorption Income Statement and Variable Costs
1. Prepare a contribution income statement and an absorption income statement. If you are in doubt any cost behavior pattern, decide on the basis of whether the total cost in question will fluctuate substantially over a wide range of volume. Prepare a separate supporting schedule of indirect manufacturing costs subdivided between variable and fixed costs.
2. Suppose that all variable costs fluctuate directly in proportion to sales, and that fixed costs are unaffected over a wide range of sales. What would operating income have been if sales had been $12 million instead of $13 million. Which income statement did you use to help get your answer? Why?
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