Complex Analysis

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Author:
Patrick_OFinnigan
ID:
66064
Filename:
Complex Analysis
Updated:
2011-02-13 14:53:41
Tags:
complex analysis
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Description:
Review for Test 1.
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  1. How are Complex Numbers defined?
    • © = {a+bi or a+ib | a,b є ®; i =
    • √(-1)}
  2. Complex Number addition / subtraction?
    (a+ib) ± (c+id) = (a±c) + i(b±d)
  3. The powers of i give?
    • (i)n = {i, -1, -i, 1, ... | for n≥1}
    • i1, i2, i3, i4, ...

    This works off of mod4.
  4. The conjugate of z is denoted as what?
    • _
    • z
  5. What is the conjugate for z = a+ib?
    z = a+ib

    • _
    • z = a-ib
    • _
    • z = z when b = 0.
  6. Complex Number Multiplication?
    (a+ib)(c+id) = (ac-bd) + i(ad+bc)
  7. z = a+ib
    _
    z = a-ib
    _
    z ∙ z = ?
    • _
    • z ∙ z = a2 + b2

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