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:

|z| = √(x² + y²) = &radic( 10² + 10²) = 14.142 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:
the principal argument is the same angle but in the range -Pi to Pi radians (-180° to 180°)
x > 0 and y > 0 the point is in the 1^st quadrant (0° to 90°):

tan(θ) =

y x

=

10 10

= 1

θ = 0.785 radians = 45° to 3 dps.