A small problem with complex conjugations

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In summary, complex conjugation is the process of changing a complex number's imaginary part to its negative counterpart. It is often used in scientific research, particularly in fields such as quantum mechanics and electrical engineering, to simplify calculations and solve equations. However, there can be problems when complex conjugations are not properly considered in equations. They are only applicable to complex numbers and can be reversed by multiplying a complex number by its complex conjugate, resulting in the original complex number.
  • #1
Parnpuu
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Hi!

I have a problem with understanding an equation which is really simple.

zz*=(a2+b2)

shouldn't there be an i there if

z1z2=(a1+ib1)(a2+ib2)

is the equation correct?

If it is could someone explain to me why there is no imaginary number?

Thank You!
 
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  • #2
if z = a + bi, then z* (conjugate of z) = a - bi so

(z)(z*) = (a+bi)(a-bi) = a2 - (bi)2 = a2 -(i)2b2 = a2 -(-1)b2 = a2 + b2
 
  • #3
Yes I can see that now.

Thanks!
 

1. What is a complex conjugation?

A complex conjugation refers to the process of changing a complex number's imaginary part to its negative counterpart. For example, if a complex number is represented as a + bi, its complex conjugate would be a - bi.

2. Why is there a problem with complex conjugations?

The problem with complex conjugations arises when trying to solve certain equations involving complex numbers. This is because the complex conjugate is essential in simplifying these equations, but it is often forgotten or overlooked.

3. How can complex conjugations be used in scientific research?

Complex conjugations are commonly used in fields such as quantum mechanics and electrical engineering. They can help simplify calculations and solve equations involving complex numbers, which are often used in these fields.

4. Are complex conjugations only applicable to complex numbers?

Yes, complex conjugations are only applicable to complex numbers. This is because they involve changing the imaginary part of a complex number, which is unique to complex numbers and not found in other types of numbers.

5. Can complex conjugations be reversed?

Yes, complex conjugations can be reversed. This is because when a complex number is multiplied by its complex conjugate, the result is always a real number. Therefore, multiplying a complex number by its complex conjugate will result in the original complex number.

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