Complex numbers Ex Sheet 4

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Violeta CIT

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Violeta CIT 7 years, 5 months ago

Created this as a copy of Arithmetics of complex numbers IV.

Name	Status	Author	Last Modified
Arithmetics of complex numbers IV	draft	Newcastle University Mathematics and Statistics	20/11/2019 14:50
Complex numbers Ex Sheet 4	draft	Violeta CIT	17/10/2017 19:53
Resuelve las operaciones indicadas y exprese el resultado en la forma $a+bi$	Ready to use	Luis Hernandez	08/11/2020 01:20
Maria's copy of Arithmetics of complex numbers IV	draft	Maria Aneiros	25/05/2019 08:20
Rechnen mit komplexen Zahlen IV	Ready to use	Ulrich Görtz	08/02/2021 19:54

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Question statement

Express the following complex numbers $z$ in the form $a+bi$ .

Input $a$ and $b$ as fractions and not as decimals. Also do not include brackets in your answer.

Give any introductory information the student needs.

			Name	Type	Generated Value

s3	integer	-1
s2	integer	1
s1	integer	1
s4	integer	1
a3	integer	-4
rz3	integer	-4
c2	integer	3
c1	integer	-6
z1	number	5 + 8i
z2	number	6 + 3i
z3	number	-4 + 4i

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Description

Describe what this variable represents, and list any assumptions made about its value.

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Generated value: `integer`

-1

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Parts

Part a) Gap-fill
1. Gap Mathematical expression
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Part b) Gap-fill
1. Gap Mathematical expression
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Gap-fill

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$\displaystyle z=\simplify[!collectNumbers]{({z3}*{z2})/{z1}}$

$z=\;\;$ Unnamed gap.

Advice

$\begin{eqnarray*}z=\simplify[!collectNumbers]{({z3}*{z2})/{z1}} &=&\simplify[!collectNumbers]{({z3}*{z2}*{conj(z1)})/({z1}*{conj(z1)})}\\ &=&\simplify[!collectNumbers]{({z3*z2}*{conj(z1)})/({abs(z1)^2})}\\ &=&\simplify[!collectNumbers]{{z3*z2*conj(z1)}/{abs(z1)^2}}\\ &=& \simplify[std]{{re(z3*z2*conj(z1))}/{abs(z1)^2}+{im(z3*z2*conj(z1))}/{abs(z1)^2}*i} \end{eqnarray*}$

$\begin{eqnarray*}z= \simplify[!collectNumbers]{({z2}*{z1})}(\var{z3})^{-1} &=& \simplify[!collectNumbers]{({z2}*{z1})/{z3}}\\ &=&\simplify[!collectNumbers]{({z2}*{z1}*{conj(z3)})/({z3}*{conj(z3)})}\\ &=&\simplify[!collectNumbers]{({z2*z1}*{conj(z3)})/({abs(z3)^2})}\\ &=&\simplify[!collectNumbers]{{z2*z1*conj(z3)}/{abs(z3)^2}}\\ &=& \simplify[std]{{re(z2*z1*conj(z3))}/{abs(z3)^2}+{im(z2*z1*conj(z3))}/{abs(z3)^2}*i} \end{eqnarray*}$

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Taxonomy: mathcentre

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Violeta CIT 7 years, 5 months ago

Error in variable testing condition

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Generated value: `integer`

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Gap-fill

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Complex numbers Ex Sheet 4

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Violeta CIT 7 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`