# Modulus and argument

## Homework Statement

Find the modulus and argument of
1) cos(i)
2) -3i

## 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!

Samy_A
Homework Helper

## Homework Statement

Find the modulus and argument of
1) cos(i)
2) -3i

## 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!
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?

SteamKing
Staff Emeritus
Homework Helper

## Homework Statement

Find the modulus and argument of
1) cos(i)
2) -3i

## 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.
Why 3π/4? How many radians does it take to go around a circle one time?
if you could point me in the right direction with 1 especially that would be greatly appreciated!

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?

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?

Samy_A