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

Q1:

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

Q2:

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

Q3:

What does the modulus of a complex number represent?

Q4:

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

Q5:

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

Q6:

In what quadrant does π§ β lie?

Q7:

Find the value of Μ π given π on the Argand diagram below.

Q8:

If the number π = 8 + π is represented on Argand diagram by the point π΄ , 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 π§ + π§ ο§ ο¨ .

Q11:

The numbers in the complex plane are mapped to their product with a particular complex number π§ . 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 π§ ?

Q12:

Consider the complex number π§ = 3 β π .

Find the modulus of π§ .

Hence, find the modulus of π§ 5 .

Q13:

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

Q14:

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

Q15:

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

Q16:

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

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