any help appriciated simplify and express the following in the form a+bi?

Question

(5+12i)/(8+9i)

Answer 1

[ (5 + 12 i) (8 - 9i) ] / [ (8 + 9i) (8 - 9i) ]
[ 40 - 45 i + 96 i - 108 i ² ] / [ 64 - 81 i ² ]
[ 40 + 51 i + 108 ] / [ 64 + 81 ]
[148 + 51 i ] / (145)

Answer 2

ok, i is not a variable here, but the expression of the irrational number, the square root of negative 1.

you are NOT solving for i, because you already know that i is the square root of negative 1. so, you have to cross multiply, and you get:
(5*8) +(5*9i) + (12i*8) + (12i*9i) which becomes
40 + 45i + 96i + 108 i squared which becomes
40 + 141i - 108 (because i squared = -1, and 108 * -1 = -108), which becomes
40-108 + 141i, which simplifies to
-68 +141i

so that's your final answer, in a+ bi format: -68 +141i

Answer 3

with complex number a+ib the complex congruent is a-ib. to eliminate the complex values from the denominator multiply top and bottom by the complex congruent of the value on the denominator

so
(5+12i/8+9i) =(5+12i/8+9i) *1
=(5+12i/8+9i) *(8-9i/8-9i)
=[(5+12i)*(8-9i)]/[(8+9i)*(8-9i)]
= [40+108+(96-45)i]/(64+81-72i+72i)
= (148+51i)/(145+0i)
= (148+51i)/(145)
= 148/145 + i51/145

so in the form a+ib
a=148/145
b=51/145

Edit - I couldn't stand my incorrect spelling of denominator and had to change it heehee