What is the Modulus of the Complex Number exp(√i)?

In summary, the conversation discusses finding the absolute value of exp(√i) and the confusion over the correct solution. The correct answer is exp(√2)/2.
  • #1
unscientific
1,734
13

Homework Statement



Find |exp(√i)|.


Homework Equations





The Attempt at a Solution



I scanned my working as attached, it seems ok to me but I don't understand why it's wrong..


The answer scheme ignores the exp(i sin (pi/4) ) part and writes the answer as exp(cos (pi/4)) = exp(1/√2).

Would appreciate any help!
 

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  • #2
unscientific said:

Homework Statement



Find |exp(√i)|.

Homework Equations



The Attempt at a Solution



I scanned my working as attached, it seems ok to me but I don't understand why it's wrong..

The answer scheme ignores the exp(i sin (pi/4) ) part and writes the answer as exp(cos (pi/4)) = exp(1/√2).

Would appreciate any help!
attachment.php?attachmentid=48368&d=1339770269.jpg


Isn't cos(π/4) = (√2)/2 ?
 
  • #3
just discovered my mistake! thanks anyway guys :)
 
  • #4
initially i was wondering why they ignored the complex part, but it works out to become this:
 

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  • #5
sorry for the trouble!
 

1. What is the modulus of a complex number?

The modulus of a complex number is the distance of the number from the origin on the complex plane. It is also known as the magnitude or absolute value of the complex number.

2. How do you find the modulus of a complex number?

To find the modulus of a complex number, you can use the Pythagorean theorem. The modulus is the square root of the sum of the squares of the real and imaginary parts of the complex number.

3. What is the significance of the modulus of a complex number?

The modulus of a complex number represents its magnitude and direction in the complex plane. It can also be used to find the polar form of the complex number, which can be helpful in performing certain mathematical operations.

4. Can the modulus of a complex number be negative?

No, the modulus of a complex number is always a positive real number. This is because it represents the distance from the origin, which cannot be negative.

5. How is the modulus of a complex number related to its conjugate?

The modulus of a complex number is equal to the modulus of its conjugate. This means that the distance from the origin to the complex number is the same as the distance from the origin to its conjugate on the complex plane.

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