Exercises for Question Type 1: Drawing complex numbers on the Argand diagram - IB | RevisionDojo

IB
Question Type 1: Drawing complex numbers on the Argand diagram

Question Type 1: Drawing complex numbers on the Argand diagram Exercises

Question 1

Plot the complex number $z = 3 - 4i$ on an Argand diagram.

[2]

Question 2

Plot the points corresponding to $z=2+i$ , $-z$ , $\overline{z}$ and $-\overline{z}$ on an Argand diagram and describe the quadrilateral formed.

[3]

Question 3

Given $z_{1}=2+3i$ and $z_{2}=-1+2i$ , plot the point representing $z_{1}+z_{2}$ on an Argand diagram.

[2]

Question 4

Let $z_{1}=1+\sqrt{3}i$ . Find the image of $z_{1}$ under multiplication by $i$ and plot both points on an Argand diagram.

[5]

Question 5

Plot the complex number $z=-3+4i$ and its reflection in the real axis on an Argand diagram.

[3]

Question 6

Sketch the locus of points $z$ in the Argand diagram satisfying $\mathrm{Re}(z)=-1$

[2]

Question 7

For $z=2+2i$ , plot $z$ and $2z$ on the same Argand diagram.

[2]

Question 8

Plot the complex number $z = 1 - i$ and its image under multiplication by $i$ on an Argand diagram.

[4]

Question 9

The vertices of a triangle in the Argand diagram are given by: $z_{1}=i,\quad z_{2}=2,\quad z_{3}=-1+2i$

Plot these points and determine the coordinates of the centroid on the diagram.

[5]

Question 10

Plot the complex number $z = 1 + 2i$ and its conjugate $\overline{z}$ on an Argand diagram.

[3]