Complex number arithmetic

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Michael Proudman

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Michael Proudman 7 years, 8 months ago

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Question statement

This question will help you to practice adding, subtracting, multiplying and dividing complex numbers in Cartesian/rectangular form. If you wish, you might like to watch this video which explains these operations and how to do problems like these.

Given the complex numbers

$z_1=\var{z1},\quad z_2=\var{z2}, \quad z_3=\var{z3}, \quad z_4=\var{z4},$

calculate the following (write your answers in Cartesian/rectangular form). Where necessary, round off your answers to 2 decimal places.

Give any introductory information the student needs.

			Name	Type	Generated Value

z1	number	6 - i
z2	number	-5 - 6i
z3	number	10 + 3i
z4	number	-5 - 5i
z4bar	number	-5 + 5i
z3z4bar	number	-65 + 35i
modz4sq	number	50
re_z3onz4	number	-1.3
im_z3onz4	number	0.7
z1plusz2	number	1 - 7i
z1minusz2	number	11 + 5i
z1z3	number	63 + 8i

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(-10..10)+random(-10..10)i

JME function reference

Description

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

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Generated value: `number`

6 - i

→ Used by:

z1minusz2
z1plusz2
z1z3

This variable doesn't seem to be used anywhere.

Advice

$z_1+z_2=(\var{z1})+(\var{z2})=\simplify{{z1}+{z2}}$

$z_1-z_2=(\var{z1})-(\var{z2})=\simplify{{z1}-{z2}}$

$z_1z_3=(\var{z1})(\var{z3})=\var{z1z3}$

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This question is used in the following exam:

Complex numbers 2024 by Katy Dobson in Katy's workspace.

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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History

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Checkpoint description

Michael Proudman 7 years, 8 months ago

Error in variable testing condition

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Generated value: `number`

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Mathematical expression

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Checking accuracy

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Complex number arithmetic

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Michael Proudman 7 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Mathematical expression

Advanced settings

Checking accuracy

Variable value generators

Pattern restriction

Variables

String restrictions

Generated value: `number`