Complex Numbers; Basics 02

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Michael Proudman

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Dr Palat Meethale Ushasree

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3 years, 2 months ago

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Dr Palat Meethale Ushasree 3 years, 2 months ago

Gave some feedback: Ready to use

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Michael Proudman 4 years, 10 months ago

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Michael Proudman 4 years, 10 months ago

Created this.

Name	Status	Author	Last Modified
Complex Numbers; Basics 02	Ready to use	Michael Proudman	08/02/2022 12:44
Complex Numbers; Addition & Subtraction 01	draft	Michael Proudman	11/01/2023 16:23
Complex Numbers; Multiplication 01 (Rect')	draft	Michael Proudman	07/12/2021 10:31

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Question statement

A complex number can be written in the form
$z=a+bi$

where $a$ and $b$ are real numbers (including $0$ ) and $i$ is an imaginary number, $i=\sqrt{-1}$ .

Generally, $a$ is called the real part of $z$ , or $\mathbb{Re}(z)$ and $b$ is called the imaginary part of $z$ or $\mathbb{Im}(z)$

Give any introductory information the student needs.

			Name	Type	Generated Value

			r1	integer	22
			i1	integer	7

			Name	Type	Generated Value

			r2	integer	7
			i2	integer	18

			Name	Type	Generated Value

			r3	integer	-9
			i3	integer	5

			Name	Type	Generated Value

			r4	integer	-9
			i4	integer	-2

			Name	Type	Generated Value

			r5	integer	-4
			i5	integer	-3

			Name	Type	Generated Value

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(2..25)

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `integer`

→ Used by:

This variable doesn't seem to be used anywhere.

Parts

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1. Gap Gap 0. Mathematical expression
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2. Gap Gap 1. Mathematical expression
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3. Gap Gap 2. Mathematical expression
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Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

State the real and imaginary parts of:

$\large z_1=\var{r1}+ \var{i1}i$

$\mathbb{Re}(z_1)=$ Gap 0. $\mathbb{Im}(z_1)=$ Gap 1.

$\large z_2=\var{r2}+ \var{i2}i$

$\mathbb{Re}(z_2)=$ Gap 2. $\mathbb{Im}(z_2)=$ Gap 3.

$\large z_3=\var{r3}+ \var{i3}i$

$\mathbb{Re}(z_3)=$ Gap 4. $\mathbb{Im}(z_3)=$ Gap 5.

$\large z_4=\simplify{{r4}+ {i4}i}$

$\mathbb{Re}(z_4)=$ Gap 6. $\mathbb{Im}(z_4)=$ Gap 7.

$\large z_5=\simplify{{r5}+ {i5}i}$

$\mathbb{Re}(z_5)=$ Gap 8. $\mathbb{Im}(z_5)=$ Gap 9.

Advice

We are asked to state the real and imaginary parts of these complex numbers.

The only things that we need to remember are:

The imaginary part $\mathbb{Im}(z)$ is the part with the $i$ ,
Either part can be $0$ , so a number like $z=15$ is still a complex number, it's just that its imaginary part $\mathbb{Im}(z)=0$ .
Likewise, a number such as $z=i9$ still has a real part, it's just that $\mathbb{Re}(z)=0$

$\large z_1=\var{r1}+ \var{i1}i$

$\mathbb{Re}(z_1)=\var{r1}$ $\mathbb{Im}(z_1)=\var{i1}$

$\large z_2=\var{r2}+ \var{i2}i$

$\mathbb{Re}(z_2)=\var{r2}$ $\mathbb{Im}(z_2)=\var{i2}$

$\large z_3=\var{r3}+ \var{i3}i$

$\mathbb{Re}(z_3)=\var{r3}$ $\mathbb{Im}(z_3)=\var{i3}$

$\large z_4=\simplify{{r4}+ {i4}i}$

$\mathbb{Re}(z_4)=\var{r4}$ $\mathbb{Im}(z_4)=\var{i4}$

$\large z_5=\simplify{{r5}+ {i5}i}$

$\mathbb{Re}(z_5)=\var{r5}$ $\mathbb{Im}(z_5)=\var{i5}$

Give a worked solution to the whole question.

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Taxonomy: mathcentre

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Checkpoint description

Dr Palat Meethale Ushasree 3 years, 2 months ago

Michael Proudman 4 years, 10 months ago

Michael Proudman 4 years, 10 months ago

A complex number can be written in the form
$z=a+bi$

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

State the real and imaginary parts of:

We are asked to state the real and imaginary parts of these complex numbers.

Loading...

Error

Complex Numbers; Basics 02

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Dr Palat Meethale Ushasree 3 years, 2 months ago

Michael Proudman 4 years, 10 months ago

Michael Proudman 4 years, 10 months ago

A complex number can be written in the formz=a+bi z=a+bi

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

State the real and imaginary parts of:

We are asked to state the real and imaginary parts of these complex numbers.

A complex number can be written in the form
$z=a+bi$

Generated value: `integer`