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MATH 4030 Matematical AnalysisSeptember 18, 2017Problem Set 21. 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| +u2⎞⎟⎠1/2,b=⎛⎜⎝|w| −u2⎞⎟⎠1/2.Prove thatz2=wifv≥0 and that(¯z)2=wifv≤0.Conclude that every complez number (with one excep-tion!) has two complex square roots.