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Express each of the following complex numbers in polar form, and plot them in the complex plane, indicating the magnitude and angle of each number.

A) $ 1 + j\sqrt{3} $

$ r = \sqrt{1^2 + \sqrt{3}^2} = \sqrt{4} = 2 $

$ \theta = arctan(\sqrt{3}/1) = arctan(\sqrt{3}) = \frac{\pi}{3} $

Therefore the polar form of this complex number is: $ 2e^{j\frac{\pi}{3}} $

B) $ -5 $

$ r = 5 $

$ \theta = \pi $

Alumni Liaison

Ph.D. on Applied Mathematics in Aug 2007. Involved on applications of image super-resolution to electron microscopy

Francisco Blanco-Silva