De Moivre's theorem 2

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Frank Doheny

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Frank Doheny

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7 years, 11 months ago

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Frank Doheny 7 years, 11 months ago

Published this.

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Frank Doheny 7 years, 11 months ago

Gave some feedback: Ready to use

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Frank Doheny 8 years, 4 months ago

Created this as a copy of DeMoivre's theorem 1.

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

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Question statement

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

Give any introductory information the student needs.

			Name	Type	Generated Value

x	integer	7
y	integer	1
n	number	0.5
theta	decimal	dec("1.418970546041639228128516171025530830078e-1")
mod	number	7.0710678119
x2	number	2.6524580875
y2	number	0.1885043923

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Generated value: `integer`

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mod
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1. Gap Gap 0. Number entry
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2. Gap Gap 1. Number entry
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$\sqrt{\var{x}+\var{y}j}=\pm(A+Bj)$

Calculate $A$ and $B$

$A$ = Gap 0.

$B$ = Gap 1.

Advice

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

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

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 $Z^{\var{n}}=|Z|^{\var{n}}\left(cos(\var{n}*\theta)+jsin(\var{n}*\theta)\right)$

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

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

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

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Frank Doheny 7 years, 11 months ago

Frank Doheny 7 years, 11 months ago

Frank Doheny 8 years, 4 months ago

Error in variable testing condition

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Generated value: `integer`

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De Moivre's theorem 2

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Frank Doheny 7 years, 11 months ago

Frank Doheny 7 years, 11 months ago

Frank Doheny 8 years, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`