DeMoivre's Theorem 1

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Peter Johnston

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Peter Johnston 7 years, 11 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

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

Question statement

Use De Moivre's theorem to calculate $(\simplify{+{x}+{y}i})^\var{n}$

Give any introductory information the student needs.

			Name	Type	Generated Value

x	integer	11
y	integer	-13
n	integer	3
theta	decimal	dec("-8.685393952858895395263291604706570185805e-1")
mod	number	17.0293863659
x2	number	-4246
y2	number	-2522

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Generated value: `integer`

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mod
theta

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1. Gap Gap 0. Number entry
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2. Gap Gap 1. Number entry
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$(\simplify{{x}+{y}i})^\var{n}=A+Bi$

Calculate $A$ and $B$

$A$ = Gap 0.

$B$ = Gap 1.

Advice

To evaluate $(\simplify{{x}+{y}i})^\var{n}$ we must first express $(\simplify{{x}+{y}i})$ in polar form.

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

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 $B=\var{y2}$

Note that the real and imaginary parts of your answer should be integers (whole numbers).

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Taxonomy: mathcentre

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Peter Johnston 7 years, 11 months ago

Error in variable testing condition

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Generated value: `integer`

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DeMoivre's Theorem 1

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`