Complex Numbers_3

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Bill Foster

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Bill Foster 55 years, 2 months ago

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Question statement

Find the following complex numbers in the form $a+bi\;$ where $a$ and $b$ are real.

Input all numbers as fractions or integers. Also do not include brackets in your answers.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	number	8 - 4i
f6	integer	6
s3	integer	1
s2	integer	-1
s1	integer	1
z1	number	3 + 6i
s6	integer	1
s5	integer	1
s4	integer	1
d6	integer	6
a3	integer	5
b3	integer	-8
c3	integer	3
e6	integer	4
z4	number	-2 + 6i
d3	integer	1
z2	number	-1 + 6i
z3	number	2 + 4i

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
s1*random(1..9)+s2*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`

8 - 4i

← Depends on:

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Mathematical expression
  Add
Part b) Gap-fill
1. Gap Mathematical expression
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Part c) Gap-fill
1. Gap Mathematical expression
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Part d) Gap-fill
1. Gap Mathematical expression
  Add

Gap-fill

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

$\var{e6*i}(\simplify[std]{{a}})\;=\;$ Unnamed gap.

Advice

The solution is given by:

$\simplify[std]{{e6*i}}(\simplify[std]{{a}})=\simplify[std]{{a*e6*i}}$

$\simplify[std]{{a}*{z4}={a*z4}}$

$\begin{eqnarray*} \simplify[std,!otherNumbers]{{a}*({a3} + {b3} * i + {c3} * i ^ 2 + {d3} * i ^ 3)}&=&\simplify[std]{{a}*{a3 + b3 * i + c3 * i ^ 2 + d3 * i ^ 3}}\\ &=&\simplify[std]{{a*(a3 + b3 * i + c3 * i ^ 2 + d3 * i ^ 3)}} \end{eqnarray*}$
d)

This can be calculated by using the formula twice, firstly to multiply out the first two sets of parentheses,

and then to multiply the result of that calculation by the third set of parentheses.

So we obtain:

$\begin{eqnarray*} (\var{a})(\var{z1})(\var{z3})&=&((\var{a})(\var{z1}))(\var{z3})\\ &=&(\var{a*(z1)})(\var{z3})\\ &=&\var{a*(z1)*(z3)} \end{eqnarray*}$

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This question is used in the following exams:

MM1 Complex numbers by Peter Rowlett in Peter's workspace.
mathcentre: Basic complex numbers by Bill Foster in Bill's workspace.
Test eksamen Matematikk 1 by Frode Naesje in Frode's workspace.
Complex Arithmetic by Hayley Bishop in Hayley's workspace.
Maths Support: Complex arithmetic by Christian Lawson-Perfect in Maths Support Wiki.
Complex Numbers by Gareth Woods in Gareth's workspace.
Sabri's copy of MM1 Complex numbers by Sabri Al-Safi in Sabri's workspace.
CN questions collection by Tatiana Tyukina in Tatiana's workspace.
Michael's copy of Maths Support: Complex arithmetic by Michael Proudman in .Complex Numbers.

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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History

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Bill Foster 55 years, 2 months ago

Error in variable testing condition

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Generated value: `number`

Parts

Gap-fill

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Complex Numbers_3

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Bill Foster 55 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`