What are two pairs of conjugates with a product of 4?
How about (3 + √5) and (3 - √5) as one of them ?
Can you see what I did there?
Can you form another? Let me know what you did.
To find two pairs of conjugates with a product of 4, let's break the problem down step by step.
First, let's define what conjugates are. In the context of mathematics, a pair of conjugate numbers refers to two numbers that have the same real part but differ in sign in their imaginary parts. In other words, for a complex number of the form a + bi, its conjugate is a - bi.
Now, let's consider the two pairs of conjugates.
Pair 1: (2 + 0i) and (2 - 0i)
Here, both numbers in the pair have the same real part (2), and their imaginary parts are zero (0i for both). The product of these two numbers, (2 + 0i) * (2 - 0i), is 4.
Pair 2: (-2 + 0i) and (-2 - 0i)
Similar to Pair 1, both numbers in Pair 2 have the same real part (-2), and their imaginary parts are zero (0i for both). The product of these two numbers, (-2 + 0i) * (-2 - 0i), is also 4.
Therefore, the two pairs of conjugates with a product of 4 are:
Pair 1: (2 + 0i) and (2 - 0i)
Pair 2: (-2 + 0i) and (-2 - 0i)