De Moivre's theorem - Square Root - Numbas at mathcentre.ac.uk

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Peter Johnston

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Peter Johnston 7 years, 11 months ago

Created this as a copy of De Moivre's theorem 2.

Name	Status	Author	Last Modified
DeMoivre's theorem 1	Ready to use	Frank Doheny	04/04/2017 08:31
De Moivre's theorem 2	Ready to use	Frank Doheny	04/04/2017 08:33
De Moivre's theorem 3	Ready to use	Frank Doheny	04/04/2017 08:42
DeMoivre's Theorem 1	draft	Peter Johnston	07/04/2017 07:29
De Moivre's theorem - Square Root	draft	Peter Johnston	07/04/2017 07:27
Maria's copy of DeMoivre's Theorem 1	draft	Maria Aneiros	25/05/2019 08:24
Maria's copy of De Moivre's theorem - Square Root	draft	Maria Aneiros	11/06/2019 06:19

There are 2 other versions that do you not have access to.

Question statement

Use De Moivre's theorem to find a square root of $Z=\var{x}+\var{y}i$

Give any introductory information the student needs.

			Name	Type	Generated Value

x	integer	12
y	integer	10
n	number	0.5
theta	decimal	dec("6.947382761967031961172741705114101030232e-1")
mod	number	15.6204993518
x2	number	3.7162144281
y2	number	1.3454551928

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Name

Data type

Value

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Description

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Generated value: `integer`

→ Used by:

mod
theta

Statement
Advice
"Unnamed part" - prompt

Parts

Gap-fill
1. Gap Gap 0. Number entry
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2. Gap Gap 1. Number entry
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Gap-fill

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

$\sqrt{\var{x}+\var{y}i}=\pm(A+Bi)$

Calculate $A$ and $B$

$A$ = Gap 0.

$B$ = Gap 1.

Advice

To evaluate $\sqrt{\var{x}+\var{y}i}$ we must first express $Z=\var{x}+\var{y}i$ in polar form.

The modulus of $\var{x}+\var{y}i$ = $\sqrt{\var{x}^2+(\var{y})^2}=\sqrt{\simplify{{x^2}+{y}^2}}$

The argument of the complex number is given by $\theta=\tan^{-1}\left(\frac{\var{y}}{\var{x}}\right)=\var{theta}$

According to De Moivre's theorem $Z^{\var{n}}=|Z|^{\var{n}}\left(\cos(\var{n}*\theta)+i\sin(\var{n}*\theta)\right)$

$(\simplify{{x}+{y}i})^\var{n}=\left(\sqrt{\simplify{{x^2}+{y}^2}}\right)^{\var{n}}\left(\cos(\simplify{{n}*{theta}})+i\sin(\simplify{{n}*{theta}})\right)$

= $\simplify{{x2}+{y2}i}$

$A=\var{x2}$ and $B=\var{y2}$

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Part	Test	Passed?
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De Moivre's theorem - Square Root

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

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Checkpoint description

Peter Johnston 7 years, 11 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

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Error

De Moivre's theorem - Square Root

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Peter Johnston 7 years, 11 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`