- #1
robertjford80
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Homework Statement
The Attempt at a Solution
do you see where it sees sqrt((1-i)(1+i)+9)?
It should be (1+i)(1+i)
Why isn't it?
Understanding Complex Numbers in Dot Product Calculations
- Thread starter robertjford80
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SUMMARY
The discussion focuses on the calculation of the dot product involving complex numbers, specifically addressing the expression sqrt((1-i)(1+i)+9). Participants clarify that the correct expression should be (1+i)(1+i) instead. The complex inner product is defined using the conjugate, represented as
- Understanding of complex numbers and their properties
- Familiarity with the concept of inner products
- Knowledge of conjugates in complex arithmetic
- Basic algebraic manipulation skills
- Study the properties of complex conjugates in vector spaces
- Learn about the geometric interpretation of complex inner products
- Explore applications of complex numbers in physics and engineering
- Investigate the differences between real and complex vector spaces
Students studying linear algebra, mathematicians interested in complex analysis, and anyone working with vector spaces involving complex numbers.
do you see where it sees sqrt((1-i)(1+i)+9)?
It should be (1+i)(1+i)
Why isn't it?
- #2
tiny-tim
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hi robertjford80! 
the complex inner product is defined with a conjugate on one side …
<a|b> = a*.b
(for real vectors, it makes no difference, so this isn't a different definition, it's the same as for real vectors
)
robertjford80 said:
the complex inner product is defined with a conjugate on one side …
<a|b> = a*.b
(for real vectors, it makes no difference, so this isn't a different definition, it's the same as for real vectors
)- #3
robertjford80
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ok thanks.