Question

Divide: 5 + 2i by 3 + 4i.(23 + 14i)/25(23 - 14i)/25(7 + i)/25(7 - i)/25

Answer 1

Given:

`(5+2i)/(3+4i)`

Required:

We need to divide 5+2i by 3+4i.

Step-by-step explanation:

The conjugate of 3+4i is 3-4i.

Multiply and divide the given expression by 3-4i

`=((5+2\imaginaryI)(3-4i))/((3+4\imaginaryI)(3-4i))`
`Use\text{ }(a+b)(a-b)=a^2-b^2.`
`=(5(3-4i)+2\imaginaryI(3-4i))/((3^2-(4i)^2))`
`=(5(3)-5(4i)+2\imaginaryI(3)-2i(4i))/(9-(-16))`
`=(15-20i+6i-8(-1))/(9+16)`
`=(15-14i+8)/(25)`
`=(23-14i)/(25)`

Final answer:

`(23-14i)/(25)`