SOLUTION: Consider the following sequence of complex numbers: (3 − 2i) , (3 − 2i)i, (3 − 2i)i^2, (3 − 2i)i^3, (3 − 2i)i^4 a) Plot the sequence on the complex

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Question 1014818: Consider the following sequence of complex numbers:
(3 − 2i) , (3 − 2i)i, (3 − 2i)i^2, (3 − 2i)i^3, (3 − 2i)i^4
a) Plot the sequence on the complex number plane.
b) Describe the geometric effect of multiplying by i.
c) Describe the geometric meaning of i^2= -1
Answer by ikleyn(52795)   (Show Source): You can put this solution on YOUR website!
.
a) all these points lie in the complex plane on the circle of the radius 5 with the center at the origin of coordinate system (z=0). 

    I will not plot them. Please do it yourself.


b) The geometric effect of multiplication by "i" is rotation in the angle  (90 degrees) anti-clockwise.


c) The geometric meaning of  = -1 is in that the multiplication of complex numbers by "i" two times is the same 
    as rotation of the complex plane in angle  (180 degrees) anti-clockwise.

You may want to look into my lessons on complex numbers in this site
REVIEW of lessons on complex numbers.


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