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

  1. May 13, 2008 #1
    URGENT: Complex Numbers Problems: HELP NEEDED FOR MY FINAL EXAM!!?

    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!
     
  2. jcsd
  3. May 13, 2008 #2

    Defennder

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    I seriously doubt anyone will help you if you don't show your attempt.
     
  4. May 13, 2008 #3
    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
     
  5. May 13, 2008 #4

    cristo

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    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.
     
  6. May 13, 2008 #5

    dx

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    Whats the distance between the origin and [tex] a + ib [/tex]?
     
  7. May 13, 2008 #6
    The distance between the origin and a + ib = |a + bi| = sqrt(a^2 + b^2)
     
  8. May 13, 2008 #7

    dx

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    So, whats the distance between two arbitrary points, a +ib and c +id?
     
  9. May 13, 2008 #8
    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
    = ???
     
  10. Oct 1, 2009 #9
    Re: URGENT: Complex Numbers Problems: HELP NEEDED FOR MY FINAL EXAM!!?

    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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