Answer: 65
Explanation:
When you multiply a complex number by its conjugate, you eliminate the imaginary part and end up with a real number.
In this case, the complex number is 4-7i. To find its conjugate, we just need to change the sign of the imaginary part. So the conjugate of 4-7i is 4+7i.
Now, let's multiply 4-7i by its conjugate:
(4-7i)(4+7i)
To multiply these two complex numbers, we can use the distributive property or the FOIL method:
(4)(4) + (4)(7i) + (-7i)(4) + (-7i)(7i)
16 + 28i - 28i - 49i^2
Now, we know that i^2 is equal to -1, so we can substitute that:
16 + 28i - 28i - 49(-1)
16 + 28i - 28i + 49
Combining like terms, we have:
16 + 49
Which simplifies to:
65
So, the result when you multiply 4-7i by its conjugate is 65.
Therefore, the correct answer is B.