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

by raladin
Tags: complex, exam, final, numbers, urgent
 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!
 HW Helper P: 2,618 I seriously doubt anyone will help you if you don't show your attempt.
 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
Mentor
P: 8,262

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

 Quote by raladin 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.
 PF Patron HW Helper P: 1,955 Whats the distance between the origin and $$a + ib$$?
 P: 4 The distance between the origin and a + ib = |a + bi| = sqrt(a^2 + b^2)
 PF Patron HW Helper P: 1,955 So, whats the distance between two arbitrary points, a +ib and c +id?
P: 63
 Quote by raladin 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
= ???
 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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