1. Explain how complex numbers combine under addition and division. Include both algebraic and graphical interpretations in your responses.

Addition: (-2+i) + (2+3i) Division: (8+4i) / (2+2i)

The graphical interpretation should demonstrate how to add and divide complex numbers solely using the graph of each complex number (not based upon the algebraic computation).

Make sure the graphical aspect of complex addition captures the visual pattern that occurs when two complex numbers are added. It must show the relationship between the summands and the resulting sum.

The visual relationship in the graphical interpretation of division between the divisor and dividend and the quotient must also be evident in the graph.

2. Use the following to complete this exercise:

Let x=r(cos u + i sin u) Let y=t(cos v + i sin v)

Prove that xy=rt(cos(u+v) + i sin(u+v))

Provide a correct proof that includes written justification for each step showing the following:

a. The angle (or argument) of the product xy is (u+v). b. The radius (or modulus) of the product xy is rt.

Please relate your conclusion to the radius of xy.

Show the computation of their product and rewrite using algebraic properties.

Subject | Mathematics |

Due By (Pacific Time) | 06/30/2013 12:00 am |

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