Why Does Setting m=0 Matter in Calculating Complex Numbers?

In summary, The conversation discusses a problem finding values of complex numbers and provides two examples with different answers from the book. The speaker mentions that the book answers are similar to Wolfram Alpha's answers and expresses confusion about when to set m=0 and when to keep it in the answers. The speaker advises keeping m in the answer unless the problem specifically states otherwise, such as when using logarithms or inverse trigonometric functions.
  • #1
ahmed markhoos
49
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Hi,I'm facing a problem finding the values of complex numbers, I'll put two examples then I'll explain the issue.

ex1: [tex] (-e)^{iπ} [/tex] , my answer is [tex] (-e)^{π^2±2mπ^2} [/tex] The book answer is [tex] (-e)^{π^2} [/tex]

ex2: [tex] e^{2 arctanh(i)} [/tex] , my answer is [tex] e^{[iπ/2±mπ/2]} = ie^{±mπ/2} [/tex] The book answer is [tex] i [/tex]

just to mention that the book answer are exactly like wolfram alpha's answers, the problem is that the answers were set as m=0 while they didn't do the same thing for other problems, When can I set m=0 and when I cannot do that?
 
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  • #2
ahmed markhoos said:
When can I set m=0 and when I cannot do that?
Keep the m if you need some logarithm or inverse trigonometric function somewhere, unless the problem statement specifies the branch you are supposed to use.
 
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Likes ahmed markhoos

FAQ: Why Does Setting m=0 Matter in Calculating Complex Numbers?

1. What are complex numbers?

Complex numbers are numbers that have both a real part and an imaginary part. They are usually written in the form a + bi, where a is the real part and bi is the imaginary part with i being the square root of -1.

2. What is the purpose of using complex numbers?

Complex numbers are used to represent and solve problems that involve both real and imaginary quantities. They are particularly useful in physics, engineering, and other scientific fields.

3. How do you add and subtract complex numbers?

To add or subtract complex numbers, you simply add or subtract the real parts and the imaginary parts separately. For example, (3 + 2i) + (1 + 4i) = (3 + 1) + (2i + 4i) = 4 + 6i.

4. How do you multiply and divide complex numbers?

To multiply complex numbers, you use the FOIL method, just like when multiplying binomials. For division, you multiply the numerator and denominator by the complex conjugate of the denominator and simplify. For example, (2 + 3i) / (1 - 2i) = (2 + 3i)(1 + 2i) / (1 - 2i)(1 + 2i) = (2 + 4i + 3i - 6) / (1 + 4) = (-4 + 7i) / 5.

5. Can complex numbers have negative exponents?

Yes, complex numbers can have negative exponents. To evaluate a negative exponent, you can use the rule that a negative exponent is equal to 1 divided by the number raised to the positive exponent. For example, (2 + 3i)^-2 = 1 / (2 + 3i)^2 = 1 / (4 + 12i + 9i^2) = 1 / (4 + 12i - 9) = 1 / (-5 + 12i).

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