# Modulus and argument

1. May 13, 2016

### struggles

1. The problem statement, all variables and given/known data
Find the modulus and argument of
1) cos(i)
2) -3i

2. Relevant equations

3. The attempt at a solution
1) So for question 1 i tried
cos(i) = ½(ei2 + e-i2) = ½(e-1 + e) . However this doesn't (as far as I can see!) lead me to the right answer. I was aiming to get it in the form reix where r is the modulus and x the argument.

for 2) I basically just drew an argand diagram and found the radius to be 3 and the argument 3/4pi.

if you could point me in the right direction with 1 especially that would be greatly appreciated!

2. May 13, 2016

### Samy_A

Concerning 1: what you have done is the right direction.
cos(i) = ½(e-1 + e) is correct.
Now the question is: why do you think this is not in the form reix?

3. May 13, 2016

### SteamKing

Staff Emeritus
Why 3π/4? How many radians does it take to go around a circle one time?

4. May 13, 2016

### struggles

I was thinking it contains no term with i. But would ½(e-1 + e) be equal to the modulus and have an argument of o?

5. May 13, 2016

### Samy_A

Exactly.

6. May 13, 2016

### struggles

Oops 3π/2?

7. May 13, 2016

Thank you!