Division of Complex Numbers

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

Use the green slider to see how the quotient of two complex numbers is built from from a triangle of the first complex number.

&bull What do the two triangles have in common and what is different?

Move the blue points (Z₁ and Z₂) to find the quotient of the Complex Numbers below and write their results:

(2+4i) ÷ (4-2i)
(1-4i) ÷ (3+i)
(5+i) ÷ (-2-i)
(-6+10i) ÷ 5
(4-2i) ÷ i

Investigates and explains what happens when ...

... a complex is divided by its opposite
... a complex is divided by a real number (with no imaginary part)
... a complex is divided by the imaginary unit i.

And if we work with polar coordinates? Look at the figure below:

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

What is the relationship between modules z₁, z₂ and z₁ ÷ z₂ ?

What will be the result of the following ratios of complex numbers? To view, right click the blue points (Z₁ and Z₂) of each complex number, select Redefine and change the coordinates.

15_150° ÷ 2_80°
6_225° ÷ 3_75°
6_225° ÷ 1_90°
6_225° ÷ 2_0°
4_60° by its conjugate.
3_150° by its opposite.

... a complex is divided by its opposite
... a complex is divided by a real number (with no imaginary part)
... a complex is divided by the imaginary unit i.

Created with GeoGebra by Manuel Sada Allo (March 2008) and adapted by Steven Lapinski