Lesson: Argand Diagram

Find the value of given on the Argand diagram below.

Given that the complex number is represented by the point on the Argand diagram below, find .

What does the modulus of a complex number represent?

What complex number lies at the midpoint of and on the given complex plane?

Describe the geometric transformation that maps every complex number to its conjugate .

In what quadrant does lie?

Find the value of given on the Argand diagram below.

If the number is represented on Argand diagram by the point , determine the Cartesian coordinates of that point.

Describe the geometric transformation that occurs when numbers in the complex plane are mapped to their sum with .

Using the Argand diagram shown, find the value of .

The numbers in the complex plane are mapped to their product with a particular complex number . Given that this transforms the complex plane by a dilation with centre the origin followed by a rotation by radians about the origin, what kind of number is ?

Find the complex number such that lies at the midpoint of and when they are represented on a complex plane.

Given that , find the principal argument of rounded to the nearest two decimal places.

Find the possible real values of such that the distance between the complex number and the complex number is 5.

Given that , find the principal argument of rounded to the nearest two decimal places.