Answer:
(d) 7/25 -(24/25)i
Step-by-step 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.
[tex]\dfrac{4-3i}{4+3i}=\dfrac{(4-3i)(4-3i)}{(4+3i)(4-3i)}=\dfrac{4^2+2(4)(-3i)+(3i)^2}{4^2-(3i)^2}=\dfrac{(16-9)-24i}{16+9}\\\\=\boxed{\dfrac{7}{25}-\dfrac{24}{25}i}[/tex]
