Blathnaid's copy of Modulus and argument complex numbers

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Blathnaid Sheridan 6 years, 5 months ago

Created this as a copy of Modulus and argument complex numbers.

Name	Status	Author	Last Modified
Modulus and argument complex numbers	Ready to use	Newcastle University Mathematics and Statistics	07/04/2023 08:05
Blathnaid's copy of Modulus and argument complex numbers	draft	Blathnaid Sheridan	25/11/2019 14:17
Maria's copy of Modulus and argument complex numbers	draft	Maria Aneiros	25/05/2019 08:20
Modulus and argument calculations	Ready to use	Shaheen Charlwood	27/10/2022 18:54

There are 32 other versions that do you not have access to.

Question statement

Find the modulus and argument (in radians) of the following complex numbers, where the argument lies between $-\pi$ and $\pi$ .

When calculating the argument pay particular attention to the quadrant in which the complex number lies.

Input all answers to 3 decimal places.

Give any introductory information the student needs.

			Name	Type	Generated Value

ans1	number	4.243
ans2	number	5.000
ans3	number	9.055
ans4	number	8.246
b4	integer	9
b1	integer	3
b2	integer	4
b3	integer	-8
d4	integer	2
d2	integer	-9
q1	string	The complex number is in the f
q3	string	The complex number is in the t
q2	string	The complex number is in the s
q4	string	The complex number is in the f
s3	integer	1
s2	integer	1
s1	integer	1
s7	integer	-1
s6	integer	-1
s5	integer	1
s4	integer	-1
m4	string	The complex number is in the f
m1	string	The complex number is in the f
z2	number	-3 + 4i
m3	string	The complex number is in the t
arg1	number	0.785
z3	number	-1 - 9i
arg2	number	2.214
arg3	number	-1.681
tol	number	0.001
arg4	number	-1.326
m2	string	The complex number is in the s
a1	integer	3
a3	integer	2
s8	integer	-1
a4	integer	-8
z4	number	2 - 8i
z5	number	-8 + 9i
z6	number	1 + 2i
z1	number	3 + 3i
c2	integer	-1
c4	integer	1
f	integer	1
n	integer	4
a2	integer	-3
t	integer	4

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
precround(abs(z1),3)

JME function reference

Description

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

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Generated value: `number`

4.243

← Depends on:

→ Used by:

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
Part b) 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.

$|\var{z1}|=\;\;$ Gap 0., $\arg(\var{z1})=\;\;$ Gap 1. radians

Input both answers to 3 decimal places.

Advice

Note that the arguments $\theta$ of the complex numbers are in radians and have to be in the range $-\pi < \theta \le \pi$ .

You have to be careful with using a standard calculator when you are finding the argument of a complex number.

If $z=a+bi=r(\cos(\theta)+i\sin(\theta))$ then we have: $r\cos(\theta)=a,\;\;r\sin(\theta)=b$ and so $\tan(\theta) = b/a$ .

Using a calculator to find the argument via $\arctan(b/a)$ works in the range $-\pi < \theta \le \pi$ when the complex number is in the first or fourth quadrants – you get the correct value.

However, The calculator gives the wrong value for complex numbers in the other quadrants.

Complex number in the Second Quadrant.

Since $\arctan(b/a)$ does not distinguish between the second and fourth quadrants and the calculator gives the argument for the fourth quadrant you have to add $\pi$ onto the calculator value.

Complex number in the Third Quadrant.

Since $\arctan(b/a)$ does not distinguish between the first and third quadrants and the calculator gives the argument for the first quadrant you have to take away $\pi$ from the calculator value.

a)Modulus.

$\begin{eqnarray*} |\var{z1}|&=&\sqrt{(\var{a1})^2+(\var{b1})^2}\\ &=& \var{abs(z1)}\\ &=&\var{ans1} \end{eqnarray*}$ to 3 decimal places.

Argument.

{m1}

Hence we see that:

$\begin{eqnarray*} \arg(\var{z1}) &=& \var{arg(z1)}\\ &=& \var{arg1}\; \mbox{radians} \end{eqnarray*}$ to 3 decimal places.

b)Modulus.

$\begin{eqnarray*} |\var{z2}|&=&\sqrt{(\var{a2})^2+(\var{b2})^2}\\ &=& \var{abs(z2)}\\ &=&\var{ans2} \end{eqnarray*}$ to 3 decimal places.

Argument.

{m2}

Hence we see that:

$\begin{eqnarray*} \arg(\var{z2}) &=& \var{arg(z2)}\\ &=& \var{arg2}\; \mbox{radians} \end{eqnarray*}$ to 3 decimal places.

c)Modulus.

$\begin{eqnarray*} |\var{z3}|&=&\sqrt{(\var{c2})^2+(\var{d2})^2}\\ &=& \var{abs(z3)}\\ &=&\var{ans3} \end{eqnarray*}$ to 3 decimal places.

Argument.

{m3}

Hence we see that:

$\begin{eqnarray*} \arg(\var{z3}) &=& \var{arg(z3)}\\ &=& \var{arg3}\; \mbox{radians} \end{eqnarray*}$ to 3 decimal places.

d)Modulus.

$\begin{eqnarray*} |\var{z4}|&=&\sqrt{(\var{a3})^2+(\var{b3})^2}\\ &=& \var{abs(z4)}\\ &=&\var{ans4} \end{eqnarray*}$ to 3 decimal places.

Argument.

{m4}

Hence we see that:

$\begin{eqnarray*} \arg(\var{z4}) &=& \var{arg(z4)}\\ &=& \var{arg4}\; \mbox{radians} \end{eqnarray*}$ to 3 decimal places.

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This question is used in the following exam:

MATH1601 CA2 Semester 1 by Blathnaid Sheridan in Blathnaid's workspace.

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Blathnaid's copy of Modulus and argument complex numbers

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Blathnaid Sheridan 6 years, 5 months ago

Error in variable testing condition

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Generated value: `number`

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Gap-fill

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Blathnaid's copy of Modulus and argument complex numbers

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Blathnaid Sheridan 6 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`