Expand complex conjugates

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Question statement

Question 1

Give any introductory information the student needs.

			Name	Type	Generated Value

z1	number	-2 - 3i
z2	number	-2 + 3i
z1z2	number	13
rez1	number	-2
rez2	number	-2
imz1	number	-3
imz2	number	3

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(1..9)*sign(random(-1,1))+sign(random(-1,1))*random(1..9)*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`

-2 - 3i

→ Used by:

imz1
rez1
rez2
z1z2
z2

Advice
"Unnamed part" - prompt

Advice

To expand $(\var{z1})(\var{z2})$ you expand the brackets as follows

$(\var{z1})(\var{z2})=(\var{re(z1)})^2+(\simplify{{imz1}i})(\simplify{{imz2}i})+(\simplify{{imz1}i})(\var{re(z2)})+(\simplify{{imz2}i})(\var{re(z1)})$

Notice that $(\simplify{{imz1}i})(\var{re(z2)})+(\simplify{{imz2}i})(\var{re(z1)})=0$

Also remembering that $i^2=-1$ you can simplify $(\simplify{{imz1}i})(\simplify{{imz2}i})=(\var{im(z1)})(\var{im(z2)})(i^2)=(\var{im(z1)})(\var{im(z2)})(-1)$ and now get

$\begin{align} (\var{z1})(\var{z2}) &=(\var{re(z1)})^2+(\var{im(z1)})(\var{im(z2)})(-1) \\ &=\var{z1z2} \end{align}$

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This question is used in the following exams:

Complex Numbers 1 by Mike Phipps in Maths for Maths.
NCM4 FE-F2022 UNIT 8 All by Terry Young in NCM4 FINAL EXAM Fall 2022.
NCM4 FE-F2022 UNIT 8 Complex Numbers by Terry Young in NCM4 FINAL EXAM Fall 2022.

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Mike Phipps 3 years, 5 months ago

Mike Phipps 3 years, 5 months ago

Mike Phipps 3 years, 5 months ago

Mike Phipps 3 years, 5 months ago

Mike Phipps 3 years, 5 months ago

Mike Phipps 3 years, 5 months ago

Mike Phipps 3 years, 5 months ago

Mike Phipps 3 years, 5 months ago

Mike Phipps 3 years, 5 months ago

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Generated value: `number`

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Number entry

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Expand complex conjugates

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Mike Phipps 3 years, 5 months ago

Mike Phipps 3 years, 5 months ago

Mike Phipps 3 years, 5 months ago

Mike Phipps 3 years, 5 months ago

Mike Phipps 3 years, 5 months ago

Mike Phipps 3 years, 5 months ago

Mike Phipps 3 years, 5 months ago

Mike Phipps 3 years, 5 months ago

Mike Phipps 3 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Number entry

Advanced settings

Generated value: `number`