Polar form of a complex number

Error

There was an error loading the page.

Contributors

Feedback

From users who are not members of Content created by Newcastle University :

Bill Foster

said

Ready to use

6 years, 2 months ago

History

○

Bill Foster 6 years, 2 months ago

Gave some feedback: Ready to use

○

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Created this.

Name	Status	Author	Last Modified
Polar form of a complex number	Ready to use	Newcastle University Mathematics and Statistics	20/11/2019 14:50
Simon's copy of Polar form of a complex number	draft	Simon Thomas	13/05/2019 15:41
Polar form of a complex number	draft	Xiaodan Leng	10/07/2019 22:22

There are 7 other versions that do you not have access to.

Question statement

Write the complex number $z=\var{z}$ in polar form $z=r\mathrm{e}^{i\theta}$ , with $r>0$ , $-\pi<\theta\leqslant\pi$ , by calculating $r$ and $\theta$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

a	number	0
argz	number	1.571
b	number	5
absz	number	5.000
tol	number	0.001
z	number	5i

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(0..5)*sign(random(-1,1))

JME function reference

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: `number`

→ Used by:

This variable doesn't seem to be used anywhere.

Parts

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

Gap-fill

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

$r=$ Unnamed gap (Enter your answer to 3 d.p.)

Advice

To write a complex number $z=a+bi$ in polar form $z=r\mathrm{e}^{i\theta}$ , we calculate the modulus $r = \lvert z \rvert$ and argument $\theta = \arg(z)$ .

Hence

$r=\lvert z \rvert=\sqrt{a^2+b^2}=\sqrt{(\var{a})^2+(\var{b})^2}=\var{absz}\;\text{to 3d.p.}$

and, in general,

$\theta=\arg(z)=\arctan\left(\frac{b}{a}\right).$

If $a=0$ , however, then $\mathrm{Re}(z)=0$ , so $\arg(z)=\pm\frac{\pi}{2}$ , depending on whether $\mathrm{Im}(z)$ is positive or negative.

In this case $a=\var{a}$ , and $b=\var{b}$ , so $\arg(z)=\var{argz}$ .

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
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet

This question is used in the following exams:

Complex variables by Newcastle University Mathematics and Statistics in Content created by Newcastle University.
End of term Review by Fouzia Ouali in Fouzia's workspace.
Complex numbers practice by Simon Lambert in Simon's workspace.
Simon's copy of Complex numbers practice by Simon Lambert in Simon's workspace.
demonstration by Timur Zaripov in Timur's workspace.
Quiz2 by Matt Falk in Matt's workspace.
Formative Assessment ENG1501 by Zepeng Liu in Zepeng's workspace.

Loading...

Error

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Bill Foster 6 years, 2 months ago

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: `number`

Parts

Gap-fill

Loading...

Error

Polar form of a complex number

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Bill Foster 6 years, 2 months ago

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`