MYTUTOR SUBJECT ANSWERS

62 views

Convert the general complex number z=x+iy to modulus-argument form.

Modulus-argument form implies that we should express z in terms of its straight line distance from the origin and the angle this straight line would make with the x axis. This is expressed as z = r ei*theta where r is the modulus and theta is the argument. We thus wish to express r and theta in terms of x and y.

This problem is best solved visually by considering an Argand diagram for the general complex number, z. In this way we can see that z is represented as a point x units along the x-axis and y units along the y-axis, forming a right angled triangle with the vertical and horizontal.

As with any right angled triangle, using Pythagoras, we can see that the length of the hypotenuse (I.e. the distance from the origin, the modulus) is given by r = sqrt(x2+y2). Similarly, using basic trigonometry we can also see that the angle between this line and the x axis (theta, the argument) is given by theta = arctan(y/x).

This means that in modulus-argument form:

z = sqrt(x2+y2) exp(i*arctan(y/x))

Ben H. A Level Further Mathematics  tutor, GCSE Further Mathematics  ...

1 month ago

Answered by Ben, an A Level Further Mathematics tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist

67 SUBJECT SPECIALISTS

£20 /hr

Tejan S.

Degree: Economics (Bachelors) - LSE University

Subjects offered: Further Mathematics , Maths+ 2 more

Further Mathematics
Maths
Economics
-Personal Statements-

“Hi everyone! My name is Tejan Shah and I am an Economics student at the London School of Economics looking to teach Economics, Mathematics and Further Mathematics A-Levels and GCSE, as well as provide significant assisstance with pers...”

£20 /hr

Mrinank S.

Degree: Engineering (Masters) - Cambridge University

Subjects offered: Further Mathematics , Physics+ 5 more

Further Mathematics
Physics
Maths
Economics
Chemistry
.PAT.
-Oxbridge Preparation-

“Hey there! I'm a second year undergraduate student at the University of Cambridge, studying Engineering. I am really passionate about using science and maths to make the world around us a better place.  I am a patient and friendly tu...”

£30 /hr

Louis S.

Degree: Mathematics (Bachelors) - Cambridge University

Subjects offered: Further Mathematics , Physics+ 6 more

Further Mathematics
Physics
Maths
Extended Project Qualification
.STEP.
.MAT.
-Personal Statements-
-Oxbridge Preparation-

“ second year undergraduate at the University of Cambridge, studying for a B.A. in Mathematics, having received A*s in A-Level Mathematics, Further Mathematics (Edexcel) and Physics (AQA)”

About the author

Ben H.

Currently unavailable: for new students

Degree: Theoretical Physics (Masters) - Birmingham University

Subjects offered: Further Mathematics , Science+ 2 more

Further Mathematics
Science
Physics
Maths

“I am a third year Theoretical Physics student at the University of Birmingham. I am passionate about all things physics  and am particularly keen on anything with a strong mathematical element. I am very patient and have a real interes...”

You may also like...

Posts by Ben

Convert the general complex number z=x+iy to modulus-argument form.

Find the possible values of x for x^2 = 36-5x.

Give examples of how the photoelectric effect supports the particle nature of light and defies the wave theory.

What is centripetal force?

Other A Level Further Mathematics questions

How to determine the modulus of a complex number?

Understanding differentiation from first principle.

The curve C has polar equation 'r = 3a(1 + cos(x)). The tangent to C at point A is parallel to the initial line. Find the co-ordinates of A. 0<x<pi

How do I do a proof by induction?

View A Level Further Mathematics tutors

Cookies:

We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok