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

1. May 13, 2008

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. May 13, 2008

### Defennder

3. May 13, 2008

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

4. May 13, 2008

### cristo

Staff Emeritus
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.

5. May 13, 2008

### dx

Whats the distance between the origin and $$a + ib$$?

6. May 13, 2008

The distance between the origin and a + ib = |a + bi| = sqrt(a^2 + b^2)

7. May 13, 2008

### dx

So, whats the distance between two arbitrary points, a +ib and c +id?

8. May 13, 2008

### BrendanH

Not true for all N (the natural numbers i.e. 1, -1, 2, -2, etc).
i^4 = (i^2)^2
= (-1)^2
= ???

9. Oct 1, 2009