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

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!

## Answers and Replies

Defennder
Homework Helper
I seriously doubt anyone will help you if you don't show your attempt.

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
Staff Emeritus
Science Advisor
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
Homework Helper
Gold Member
Whats the distance between the origin and $$a + ib$$?

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

dx
Homework Helper
Gold Member
So, whats the distance between two arbitrary points, a +ib and c +id?

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
= ???

hey,in urgent need ,got exams tomorrow
can anyone help with these ques,
if sin(a+ic)=tanb+isecb,prove that cos2acosh2c=3