The product (5+i)(5−i) is a real number, 26. What are the factors (5+i) and (5−i) called?
imaginary units**
complex numbers
complex conjugates
imaginary numbers
My answer is A but im not sure if thats right
Your answer is correct! The factors (5+i) and (5-i) are called complex conjugates. Complex conjugates have the same real part but opposite signs for their imaginary parts. In this case, the conjugate of (5+i) is (5-i).
Your answer is incorrect. The correct answer is C, complex conjugates.
To understand why, let's expand the given expression and simplify it:
(5+i)(5−i)
= 5(5) + 5(-i) + i(5) + i(-i) (using the distributive property)
= 25 - 5i + 5i - i^2
= 25 - i^2 (since i^2 = -1)
= 25 - (-1) (substituting i^2 = -1)
= 25 + 1
= 26
From the simplification, we can see that the product (5+i)(5−i) is equal to 26, which is a real number. This means that the factors (5+i) and (5−i) are complex conjugates.
Complex conjugates are formed when a complex number has its imaginary part with opposite signs. In this case, (5+i) and (5−i) are complex conjugates because they have opposite signs for the imaginary part (i).
Therefore, the correct answer is C, complex conjugates.
nope. Try C
i is the imaginary unit.
bi is an imaginary number
a+bi is a complex number
a-bi is the conjugate of a+bi