Question

simplify: 3-4¡/3+4¡ + 3+4¡/3-4¡. Look at the picture to see what the math problem and answer options are.​

Answer 1

Remember i^2 = -1 so (4i)^2 = -16
Multiply the first fraction by (3 - 4i)/(3 - 4i) and the second fraction by (3 + 4i)/(3 + 4i)
= (3 - 4i)(3 - 4i)/(3 + 4i)(3 - 4i) + (3 + 4i)(3 + 4i)/(3 - 4i)(3 + 4i)
= (9 - 8i - 16)/(9 - -16) + (9 + 8i - 16)/(9 - -16)
= (-7 - 8i)/25 + (-7 + 8i)/25
= (-7 - 8i -7 + 8i)/25
= -14/25 which is the first option shown

Answer 2

The choice

`- (14)/(25)`

`(3 - 4i)/(3 + 4i) + (3 + 4i)/(3 - 4i) \\ \\( (3 - 4i)/(3 + 4i) *(3 - 4i)/(3 - 4i)) +( (3 + 4i)/(3 - 4i) * (3 + 4i)/(3 + 4i)) \\ \\ \frac{ - 7 - 24i}{9 - 16 {i}^(2) } + \frac{ - 7 + 24i}{9 - 16 {i}^(2) } \\ \\ ( - 7)/(9 + 16) + ( - 7)/(9 + 16) \\ \\ ( - 7)/(25) + ( - 7)/(25) = ( - 14)/(25)`

I hope I helped you^_^