Modulus and argument

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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 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!
 

Answers and Replies

  • #2
Samy_A
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Homework Helper
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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 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?
 
  • #3
SteamKing
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Science Advisor
Homework Helper
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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 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!
 
  • #4
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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?
 
  • #5
Samy_A
Science Advisor
Homework Helper
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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.
 
  • #6
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Why 3π/4? How many radians does it take to go around a circle one time?
Oops 3π/2?
 
  • #7
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