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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-> 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(52790) (Show Source):
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.
