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Operations with Complex Numbers

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1. Find the area bounded by the lines y=0, y=2 an y=sqrt(x)

2. Find the partial decomposition of:

3. Find the critical points and the inflection points of the following function:
f(x) = x^4 - 4x^3 + 10

4. Simplify the following complex expressions, expressing each in the form (a + jb)
(i) (4+j|1)+(8+j6)
(ii) (10+j5)-(-2-j4)
(iii) (3-j4)(-5-j3)
(iv) (4-j7)(6+j3)
(v) (-1+j4)^2
(vi) (p+jq)^2

5. There are four complex numbers in polar form (see attached)
(i) Sketch each complex number on an Argand diagram
(ii) Convert z1, z2, z3, z4 to their rectangular forms.
(iii) Determine the dot products of z1, z3 and z2, z4 in their polar forms
(iv) Determine (z2(dot)z3)/(z1(dot)z4) in polar form

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Solution Summary

This solution discusses operations with complex numbers and includes a sketch of complex numbers on Argand diagrams.

Solution provided by:
  • BSc, University of Bucharest
  • MSc, Ovidius
  • MSc, Stony Brook
  • PhD (IP), Stony Brook
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