Modulus and Argument of cos(i) and -3i

[struggles]

Homework Statement

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

Homework Equations

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 re^ix 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 Statement

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

Homework Equations

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 re^ix 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 re^ix?

 

[SteamKing]

Homework Statement

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

Homework Equations

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 re^ix 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!

 

[struggles]

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 re^ix?

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]

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?

Exactly.

 

[struggles]

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

Oops 3π/2?

 

[struggles]

Exactly.

Thank you!