Docsity
Docsity

Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity


Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan


Guidelines and tips
Guidelines and tips

Magnitude of Complex Number - Optics and Modern Physics - Solved Past Paper, Exams of Physics

This is the Solved Past Paper of Optics and Modern Physics which includes Transparent Sphere of Index, Principle Points, Transform Matrix, Ray Incident, Total Internal Reflection, Index of Refraction etc. Key important points are: Magnitude of Complex Number, Exponential Form, Imaginary Part, Complex Number Representation, Real Part, Ground State, Potential Height, Kinetic Energy of Electrons, Photoelectric Effect

Typology: Exams

2012/2013

Uploaded on 02/23/2013

super-malik
super-malik 🇮🇳

4.6

(14)

195 documents

1 / 1

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
3.
a) Working directly with exponentials, show that the magnitude of ˜z=Aeiωt is A.
Recall that the magnitude of a complex number ˜zis given by
|˜z|= z˜z]1/2
Using the exponential form, as instructed in the problem, gives
|˜z|=A eiωt A eiωt1/2=A21/2
Since it is assumed that Ais a real number when we write complex numbers in exponential form, we
can then simplify this to
|˜z|=A21/2=A
b) Show that the imaginary part of ˜zis given by z˜z)/2i. You do not need to use exponentials for (b).
It is probably easiest here to use the complex number representation ˜z=a+bi where ais the real part
and bis the imaginary part. Putting this into the expression above gives
(a+bi)(abi)
2i=(aa) + (bi +bi)
2i=2bi
2i=b
Given the definition of this form of complex number representation, bis the imaginary part of ˜
(z).

Partial preview of the text

Download Magnitude of Complex Number - Optics and Modern Physics - Solved Past Paper and more Exams Physics in PDF only on Docsity!

a) Working directly with exponentials, show that the magnitude of z˜ = Ae iωt is A.

Recall that the magnitude of a complex number ˜z is given by

|z˜| = [˜z ∗ z˜]

1 / 2

Using the exponential form, as instructed in the problem, gives

|z˜| =

[

A e −iωt A e iωt

] 1 / 2

[

A

2

] 1 / 2

Since it is assumed that A is a real number when we write complex numbers in exponential form, we

can then simplify this to

|z˜| =

[

A

2

] 1 / 2

= A

b) Show that the imaginary part of z˜ is given by (˜z − ˜z ∗ )/ 2 i. You do not need to use exponentials for (b).

It is probably easiest here to use the complex number representation ˜z = a + bi where a is the real part

and b is the imaginary part. Putting this into the expression above gives

(a + bi) − (a − bi)

2 i

(a − a) + (bi + bi)

2 i

2 bi

2 i

= b

Given the definition of this form of complex number representation, b is the imaginary part of ˜(z).