Problem Set 2 - MATH 4030 Matematical Analysis Problem Set 2 1 Prove the distributive property for complex numbers 2 Show that every nonzero complex

Problem Set 2 - MATH 4030 Matematical Analysis Problem Set...

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MATH 4030 Matematical Analysis September 18, 2017 Problem Set 2 1. Prove the distributive property for complex numbers.2. Show that every nonzero complex number can be writtenin one and only one way as the product of a positive realnumber and a number of absolute value one.3. Suppose thatz=a+bi,w=u+vianda=|w| +u21/2,b=|w| −u21/2.Prove thatz2=wifv0 and that(¯z)2=wifv0.Conclude that every complez number (with one excep-tion!) has two complex square roots.

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