A complex number in the form
is said to be in rectangular, or Cartesian, form. Note that x and y are the coordinates of the point represented x+iy in the complex Cartesian plane.
Points in the complex plane can also be represented with polar coordinates. Recall that
define the relationship between polar and Cartesian coordinates. Substituting these into the rectangular form of a complex number, we get
for r≥0, 0≤θ< 2 π. θ is referred to as the argument of Z.
in polar form.
The modulus, or magnitude, of Z is defined as
It is the distance from the origin to the point (x,y). Recall that
This implies that
Product and Quotient of Complex Numbers in Polar Form
For complex numbers
Try these exercises
Solve. Round all decimals to the nearest hundredth
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