Polar form of a complex number

Error

There was an error loading the page.

Contributors

Michael Proudman

History

○

Michael Proudman 7 years, 8 months ago

Created this.

There is only one version of this question that you have access to.

There are 12 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 $-\pi<\theta\leqslant\pi$ , by calculating $r$ and $\theta$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

a	number	-2
argz	number	-2.159
b	number	-3
absz	number	3.606
tol	number	0.001
z	number	-2 - 3i

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`

-2

→ 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:

Loading...

Error

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: `number`

Parts

Gap-fill

Loading...

Error

Polar form of a complex number

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: number

Parts

Gap-fill

Generated value: `number`