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: Complex Numbers Problems: HELP NEEDED FOR MY FINAL EXAM ?

by raladin
Tags: complex, exam, final, numbers, urgent
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raladin
#1
May13-08, 12:32 PM
P: 4
Q1: Write the numbers in the form a+b:

i) (2+3i)/(1+2i) - (8+i)/(6-i)

ii) [(2+i)/(6i-(1-2i))]^2


Q2: Simplify:

i) i^11

ii) i^203


Q3: Show that the points: 1, -1/2 + (i*squareroot(3))/2, -1/2 - (i*squareroot(3))/2 are the vertexes of an equilateral triangle.


Q4: Describe:

i) | 2Z - i |= 4
ii) | Z | = 3 |Z - 1|


Q5: Write in Polar Form:

i) (1+i)/[squareroot(3)-1]

ii) -2*squareroot(3) - 2i

iii) (1-i) (-squareroot(3)*i)

iv) (-1 + squareroot(3)*i)/(2+2i)


Can you please show detailed solution for each one because I don't get the lesson.. I don't have that part in my book, and it is included in my final exam after 3 days. I hope you can help me..Thanks alot in advance!
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Defennder
#2
May13-08, 12:38 PM
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P: 2,616
I seriously doubt anyone will help you if you don't show your attempt.
raladin
#3
May13-08, 12:43 PM
P: 4
The usual method of Q1. is to multiply each fraction by the conjugate of the denominator in order to give it a real denominator... but can you please show me one solution so that I make sure?

For 2. To use the fact that i^2n = -1

For 3, To show that the distances between each point on the complex plane are equal.. but how?

On Q4, No idea

Q5 No idea

cristo
#4
May13-08, 12:47 PM
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: Complex Numbers Problems: HELP NEEDED FOR MY FINAL EXAM ?

Quote Quote by raladin View Post
The usual method of Q1. is to multiply each fraction by the conjugate of the denominator in order to give it a real denominator... but can you please show me one solution so that I make sure?
Again, I'm afraid that's not how the forums work. Why don't you have a go at simplifying the fractions and then we can give you some help if you make any mistakes.
dx
#5
May13-08, 12:48 PM
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Whats the distance between the origin and [tex] a + ib [/tex]?
raladin
#6
May13-08, 01:30 PM
P: 4
The distance between the origin and a + ib = |a + bi| = sqrt(a^2 + b^2)
dx
#7
May13-08, 01:36 PM
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So, whats the distance between two arbitrary points, a +ib and c +id?
BrendanH
#8
May13-08, 02:30 PM
P: 63
Quote Quote by raladin View Post
For 2. To use the fact that i^2n = -1[/B]
Not true for all N (the natural numbers i.e. 1, -1, 2, -2, etc).
What about i^4 ?
i^4 = (i^2)^2
= (-1)^2
= ???
blade_19
#9
Oct1-09, 11:20 PM
P: 1
hey,in urgent need ,got exams tomorrow
can anyone help with these ques,
if sin(a+ic)=tanb+isecb,prove that cos2acosh2c=3


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