- #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
- Start date
In summary, the dot product of two complex numbers is defined as (a*c + b*d), where "a" and "b" are the real parts and "c" and "d" are the imaginary parts of the complex numbers. It is used in complex number operations to find the magnitude and angle between two complex numbers, and to determine orthogonality or parallelism. It can be negative if the angle between the two numbers is greater than 90 degrees. The dot product is related to the cross product through the use of the complex conjugate. It is commonly used in physics, engineering, and mathematics to calculate work, power, and energy in AC circuits, find angles between vectors or forces, and determine similarities or differences
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
Science Advisor
Homework Helper
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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.
Related to Understanding Complex Numbers in Dot Product Calculations
1. What is the dot product of two complex numbers?
The dot product of two complex numbers, represented as (a+bi) and (c+di), is defined as (a*c + b*d), where "a" and "b" are the real parts and "c" and "d" are the imaginary parts of the complex numbers.
2. How is the dot product used in complex number operations?
The dot product is used in complex number operations to find the magnitude of a complex number, to calculate the angle between two complex numbers, and to determine the orthogonality or parallelism of two complex numbers.
3. Can the dot product of two complex numbers be negative?
Yes, the dot product of two complex numbers can be negative if the angle between them is greater than 90 degrees. This means that the two complex numbers are orthogonal or perpendicular to each other.
4. How is the dot product related to the cross product in complex numbers?
The dot product is related to the cross product in complex numbers through the use of the complex conjugate. The cross product of two complex numbers is equal to the negative of the dot product of the first complex number and the complex conjugate of the second complex number.
5. In what applications is the dot product of complex numbers used?
The dot product of complex numbers is commonly used in physics, engineering, and mathematics to calculate work, power, and energy in AC circuits, to find the angle between two vectors or forces, and to determine the similarity or difference between two complex numbers.
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