What is the conjugate of (A+iB)exp(C+iD)?

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In summary, the conjugate of (A+iB)exp(C+iD) is (A-iB)exp(C-iD). To find the conjugate of a complex number, simply change the sign of the imaginary part. The conjugate of a complex number represents the reflection of the number across the real axis on the complex plane. When simplifying (A+iB)exp(C+iD), it becomes e^A(cos(B)+isin(B))exp(C+iD) and its conjugate becomes e^A(cos(B)-isin(B))exp(C-iD). The relationship between a complex number and its conjugate is that they have the same real part but opposite imaginary parts, making their product and sum real numbers.
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henry wang
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I came across this in QM course while trying to work out the time evolution equation of a wave-packet.

##(A+iB)^{1/2}*e^{C+iD}##

*Thank you I got it: I converted A+iB to exponential form and used De Moivre theorem to find the sqrt of A+iB, and finally combined the two exponentials and worked out the conjugate.*
 
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Great work!
 

What is the conjugate of (A+iB)exp(C+iD)?

The conjugate of (A+iB)exp(C+iD) is (A-iB)exp(C-iD).

How do you find the conjugate of a complex number?

To find the conjugate of a complex number, simply change the sign of the imaginary part. For example, the conjugate of A+iB is A-iB.

What does the conjugate of a complex number represent?

The conjugate of a complex number represents the reflection of the number across the real axis on the complex plane. It has the same real part but the imaginary part has the opposite sign.

Can you simplify the expression (A+iB)exp(C+iD) and its conjugate?

Yes, you can simplify (A+iB)exp(C+iD) to e^A(cos(B)+isin(B))exp(C+iD). The conjugate would be e^A(cos(B)-isin(B))exp(C-iD).

What is the relationship between a complex number and its conjugate?

The relationship between a complex number and its conjugate is that they have the same real part but opposite imaginary parts. This means that their product is always a real number, and their sum is always a real number as well.

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