DeMoivre's theorem 1

Error

There was an error loading the page.

Contributors

Frank Doheny

Feedback

From users who are members of Complex numbers :

Frank Doheny

said

Ready to use

7 years, 11 months ago

History

○

Frank Doheny 7 years, 11 months ago

Published this.

○

Frank Doheny 7 years, 11 months ago

Gave some feedback: Ready to use

○

Frank Doheny 8 years, 4 months ago

Created this.

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 $(\simplify{+{x}+{y}j})^\var{n}$

Give any introductory information the student needs.

			Name	Type	Generated Value

x	integer	11
y	integer	-13
n	integer	5
theta	decimal	dec("-8.685393952858895395263291604706570185805e-1")
mod	number	17.0293863659
x2	number	-517484.0000000003
y2	number	1335412.0000000005

Automatically regenerate variables?

Name

Data type

Value

A random number between and (inclusive) with step size

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: `integer`

→ Used by:

mod
theta

Statement
Advice
"Unnamed part" - prompt

Parts

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

Gap-fill

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

$(\simplify{{x}+{y}j})^\var{n}=A+Bj$

Calculate $A$ and $B$

$A$ = Gap 0.

$B$ = Gap 1.

Advice

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

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

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 $B=\var{y2}$

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

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

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

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet

This question is used in the following exams:

Loading...

Error

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

Loading...

Error

DeMoivre's theorem 1

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`