Complex Numbers: Polar form

Worked Solution:

On the Argand diagram, the modulus of the complex number z is
the distance of the point (x, y) = (Re(z), Im(z)) from the origin:

r = √(x² + y²) = &radic( 5² + (–4)²) = 6.403 to 3 dps.

The argument is the angle θ that a line from the origin to the same point makes with the (positive) x-axis:
x > 0 and y < 0 the point is in the 4^th quadrant (0° to –90°):

tan(θ) =

y x

=

–4 5

= –0.80000

θ = –0.675 radians = –38.660° to 3 dps.