I Don't Know What Is This Subject Called In English But It's About Complex Numbers
it says
25 = 16 - 9 i^2 = (4 ± 3i)
But My Teacher Says
25 = 25 - 0 i^2 = (5 ± 0i)
I Think My Teacher Is Wrong , The Result Is 25 But There Will Not Be Complex Number Because ( 0i = 0)
So Is My Teacher Wrong Or Not ?
both end statements are incorrect
(4 ± 3i) means (4+3i) OR (4-3i)
it has nothing to do with the multiplication of
(4+3i)(4-3i)
which would be
16 - 9i^2
= 16 - (-9)
= 25
your teacher should have said, (probably did)
(5 + 0i)(5-0i)
= 25 - 0i^2
= 25
In mathematics, complex numbers are numbers that consist of both a real part and an imaginary part. In this case, you are given two different expressions and you are trying to determine which one is correct.
First, let's look at the two expressions given by your teacher and yourself:
Expression 1: 25 = 16 - 9i^2 = (4 ± 3i)
Expression 2: 25 = 25 - 0i^2 = (5 ± 0i)
To understand which expression is correct, we need to remember that i is the imaginary unit, defined as the square root of -1. Therefore, i^2 is equal to -1.
Let's evaluate Expression 1:
16 - 9i^2 = 16 - 9(-1) = 16 + 9 = 25
Now let's evaluate Expression 2:
25 - 0i^2 = 25 - 0(-1) = 25 + 0 = 25
Both expressions simplify to 25, so they are equivalent. However, your teacher's explanation states that the imaginary part is 0i (zero times the imaginary unit). Since any number multiplied by zero is zero, the imaginary part becomes zero.
So, in this case, your teacher is correct. The result is 25, and although it involves complex numbers, the imaginary part is indeed zero.