Lesson: Argand Diagram

In this lesson, we will learn how to identify complex numbers plotted on an Argand diagram and discover their geometric properties.

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Worksheet: Argand Diagram • 16 Questions • 1 Video

Q1:

Find the value of 𝑍 given 𝑍 on the Argand diagram below.

Q2:

Given that the complex number 𝑍 is represented by the point ( 4 , 4 ) on the Argand diagram below, find | 𝑍 | .

Q3:

What does the modulus of a complex number represent?

Q4:

What complex number lies at the midpoint of 𝑧 1 and 𝑧 2 on the given complex plane?

Q5:

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

Q6:

In what quadrant does 𝑧 lie?

Q7:

Find the value of ̄ 𝑍 given 𝑍 on the Argand diagram below.

Q8:

If the number 𝑍 = 8 + 𝑖 is represented on Argand diagram by the point 𝐴 , determine the Cartesian coordinates of that point.

Q9:

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

Q10:

Using the Argand diagram shown, find the value of 𝑧 + 𝑧 .

Q11:

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

Q12:

Consider the complex number 𝑧 = 3 𝑖 .

Find the modulus of 𝑧 .

Hence, find the modulus of 𝑧 5 .

Q13:

Find the complex number 𝑧 such that 4 + 3 𝑖 lies at the midpoint of 𝑧 and 3 4 𝑖 when they are represented on a complex plane.

Q14:

Given that 𝑍 = 9 + 3 𝑖 , find the principal argument of 𝑍 rounded to the nearest two decimal places.

Q15:

Find the possible real values of 𝑏 such that the distance between the complex number 6 + 7 𝑖 and the complex number 3 + 𝑏 𝑖 is 5.

Q16:

Given that 𝑍 = 5 + 9 𝑖 , find the principal argument of 𝑍 rounded to the nearest two decimal places.

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