Q1. Convert the complex number z = 6 + 8j to polar form.
A1. The magnitude |z|= \sqrt{6^2 + 8^2}= \sqrt{36+ 64} = \sqrt{100} = 10.
Since both x and y components are positive, the complex number is in the first quadrant.
The argument \theta = atan(\frac{8}{6}) = 0.9273, in radians. Multiply by 180/\pi to obtain the argument degrees. The value would be 53.3^\circ.
Q2, Convert to rectangular form the complex number in polar form 12 \angle 210^\circ .
A2. The complex number is in the third quadrant. This means that both components are negative.
x = 12 \cos(210^\circ) = -10.392, y = 12 \sin(210^\circ) = -6.0,from which z = -10.392 - 6j.
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