Complex number multiplication & division

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Michael Proudman

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Michael Proudman 7 years, 8 months ago

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Question statement

Given three complex numbers $Z_{1}=\var{x1}+\var{y1}j$ , $Z_{2}=\var{x2}+\var{y2}j$ and $Z_{3}=\var{x3}+\var{y3}j$

Give any introductory information the student needs.

			Name	Type	Generated Value

x1	integer	2
x2	integer	2
x3	integer	6
y1	integer	10
y2	integer	12
y3	integer	4
A	number	-10
B	number	14

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Data type

Value

A random number between and (inclusive) with step size

Description

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Generated value: `integer`

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1. Gap Gap 0. Number entry
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2. Gap Gap 1. Number entry
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Ask the student a question, and give any hints about how they should answer this part.

If $\frac{Z_{1}*Z_2}{Z_3}=A+Bj$

Input the value for $A$ Gap 0.

Input the value for $B$ Gap 1.

Advice

$\frac{Z_1*Z_2}{Z_3}=\frac{(\var{x1}+\var{y1}j)(\var{x2}+\var{y2}j)}{\var{x3}+\var{y3}j}$

= $\frac{\simplify{{x1}*{x2}}+\simplify{{x1}*{y2}}j+\simplify{{y1}*{x2}}j+\simplify{{y1}*{y2}}j^{2}}{\var{x3}+\var{y3}j}$

= $\frac{\simplify{{x1}*{x2}}+\simplify{{x1}*{y2}+{y1}*{x2}}j-\simplify{{y1}*{y2}}}{\var{x3}+\var{y3}j}$

= $\frac{\simplify{{x1}*{x2}-{y1}*{y2}}+\simplify{{x1}*{y2}+{y1}*{x2}}j}{\var{x3}+\var{y3}j}$

= $\frac{\simplify{{x1}*{x2}-{y1}*{y2}}+\simplify{{x1}*{y2}+{y1}*{x2}}j}{\var{x3}+\var{y3}j}\frac{\var{x3}-\var{y3}j}{\var{x3}-\var{y3}j}$

= $\frac{\simplify{({x1}*{x2}-{y1}*{y2})*{x3}}-(\simplify{({x1}*{x2}-{y1}*{y2})*{y3}}j)+(\simplify{({x1}*{y2}+{y1}*{x2})*{x3}}j)-\simplify{({x1}*{y2}+{y1}*{x2})*{y3}}j^{2}}{\var{x3}^{2}+\var{y3}^{2}}$

= $\frac{\simplify{({x1}*{x2}-{y1}*{y2})*{x3}+({x1}*{y2}+{y1}*{x2})*{y3}}+\simplify{({x1}*{y2}+{y1}*{x2})*{x3}-({x1}*{x2}-{y1}*{y2})*{y3}}j}{\simplify{{x3}^{2}+{y3}^{2}}}$

= $\var{A}+\var{B}j$

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Michael Proudman 7 years, 8 months ago

Error in variable testing condition

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Generated value: `integer`

Parts

Gap-fill

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Complex number multiplication & division

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Michael Proudman 7 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`