Complex numbers question!!?

basically just multiply the top and bottom by 3+4i.

((5+i)(3+4i))/((3+4i)(3-4i))

then foil the top and bottom.

(15+3i+20i+4i^2)/(9-12i+12i-16i^2)

i^2 is -1, so convert that and you get.

(11+23i)/(25)

then just divide that to get

11/25+23/25i

make it a good day

Remember that (a+bi)(a - bi) = a^2 + b^2. So you can rationalize the denominator by multiplying by its conjugate.

Take (5+i) / (3-4i), and multiply the top and bottom by 3+4i. This will give you something in the form of a+bi up top, and 9+16 = 25 on the bottom. You can then distribute the 25 to get (a/25) + (b/25)i.

[(5 + i)/(3 - 4i)]*[(3 + 4i)/(3 + 4i)]

[(5 + i)(3 + 4i)]/(9 - 16i^2)

[15 + 20i + 3i + 4i^2] (9 + 16)

(11 + 23i)/25

Remember i^2 = -1. So 4i^2 = -4.

multiply fraction by the conjugate, which is (3+4i)/(3+4i) to get

=(5+i)(3+4i)/(3-4i)(3+4i)

=(15+3i+20i+4i^2)/(9-12i+12i-16i^2)

=(11+23i)/(9+16)

=(11+23i)/25

(5+i)/(3-4i) = (5+i)(3+4i)/(3-4i)(3+4i)

=(5+i)(3+4i)/(9-16i^2) = (5+i)(3+4i)/25=(15+23i+4i^2)/25=(11+23i)/25