Problems with complex numbers.

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 \(z = -10.392 - 6j.\)