Question

Can somebody help me if you know what this is

Answer 1

(d) 7/25 -(24/25)i

Explanation:

You want the value of 4-3i divided by its conjugate.

Conjugate

The conjugate of a sum is the same sum with the sign changed.

conjugate of 4-3i is 4+3i

conjugate of 4+√2 is 4-√2

In algebra, a conjugate is often used when squaring one of the terms will make it "rational" or real (or both). That is because the product of a number and its conjugate is the difference of the squares of the parts of the sum.

(a -b)(a +b) = a² -b²

Application

You want the value of (4-3i) divided by its conjugate. Simplifying that expression will also make use of the conjugate.

`(4-3i)/(4+3i)=((4-3i)(4-3i))/((4+3i)(4-3i))=(4^2+2(4)(-3i)+(3i)^2)/(4^2-(3i)^2)=((16-9)-24i)/(16+9)\\\\=\boxed{(7)/(25)-(24)/(25)i}`