De Moivre's Theorem: $n$th roots of a complex number $(-\pi\leq \theta \leq \pi)$

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Denis Flynn

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Denis Flynn 8 years, 2 months ago

Created this as a copy of De Moivre's Theorem:

$n$ th roots of a complex number.

Name	Status	Author	Last Modified
De Moivre's Theorem: $n$ th roots of a complex number	Ready to use	Newcastle University Mathematics and Statistics	07/04/2023 08:05
De Moivre's Theorem: $n$ th roots of a complex number $(-\pi\leq \theta \leq \pi)$	draft	Denis Flynn	31/01/2017 10:57
De Moivre's Theorem: $n$ th roots of a complex number	draft	Peter Johnston	02/04/2019 11:58
Complex Numbers Ex Sheet 6 De Moivre's Theorem: $n$ th roots of a complex number	draft	Violeta CIT	17/10/2017 19:59
Christian's copy of De Moivre's Theorem: $n$ th roots of a complex number	draft	Christian Lawson-Perfect	02/04/2019 10:46
Maria's copy of De Moivre's Theorem: $n$ th roots of a complex number	draft	Maria Aneiros	25/05/2019 08:24

There are 22 other versions that do you not have access to.

Question statement

Find the $\var{n}$ th roots of $\var{z1}$ .

Important: When calculating the roots, you must use non-truncated values for the modulus and argument calculated in parts (i) and (ii) and not the approximated values, otherwise the final answer may not be correct.

For the purposes of this question all arguments of complex numbers are between $- \pi$ and $\pi$ radians.

Give any introductory information the student needs.

			Name	Type	Generated Value

q1	string	The complex number is in the f
argrn	number	5.095
q3	string	The complex number is in the t
q2	string	The complex number is in the s
q4	string	The complex number is in the f
md1	number	1.239
arg1	number	-2.034
s2	integer	-1
s1	integer	-1
targ1	number	-2.0344439358
n	integer	7
a1	integer	-2
m1	string	The complex number is in the t
t	integer	3
tol	number	0.001
ans1	number	4.472
gap	number	0.898
adj	integer	0
z1	number	-2 - 4i
argr1	number	-0.291
b1	integer	-4

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
'The complex number is in the first quadrant.'

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: `string`

The complex number is in the first quadrant.

→ Used by:

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
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3. Gap Gap 2. Number entry
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4. Gap Gap 3. Number entry
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5. Gap Gap 4. Number entry
  Add
6. Gap Gap 5. Number entry
  Add
7. Gap Gap 6. Number entry
  Add

Gap-fill

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

Find the modulus and argument of $\var{z1}$ to 3 decimal places.

(i) $|\var{z1}|\;=\;$ Gap 0., to 3 decimal places.

(ii) $\arg(\var{z1})\;=\;$ Gap 1. radians, to 3 decimal places.

Hence find the following $\var{n}$ th roots of $\var{z1}$ i.e. solve for $z$ , $z^\var{n}=\var{z1}$ .

How many roots are there? Gap 2.

All the roots have the same modulus.

Input the modulus here: Gap 3. (to 3 decimal places).

What is the argument of the root with the least argument? Gap 4. radians (to 3 decimal places)

What is the argument of the root with the greatest argument? Gap 5. radians (to 3 decimal places).

If the roots are ordered in terms of their increasing arguments, what is the angle between successive roots? Gap 6. radians (to 3 decimal places).

Advice

To be completed.

Give a worked solution to the whole question.

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There was an error which means the tests can't run:

Part	Test	Passed?
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Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
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Number entry
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Number entry
Number entry		Hasn't run yet
Number entry
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Number entry
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This question is used in the following exam:

Week 3 Applied Calculus by Denis Flynn in Denis's workspace.

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De Moivre's Theorem: $n$ th roots of a complex number $(-\pi\leq \theta \leq \pi)$

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Taxonomy: mathcentre

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Denis Flynn 8 years, 2 months ago

Error in variable testing condition

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Generated value: `string`

Parts

Gap-fill

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De Moivre's Theorem: nnth roots of a complex number (−π≤θ≤π)(-\pi\leq \theta \leq \pi)

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Denis Flynn 8 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: string

Parts

Gap-fill

De Moivre's Theorem: $n$ th roots of a complex number $(-\pi\leq \theta \leq \pi)$

Generated value: `string`