# Simplify (8i + 7)(9i + 10)/ (3i +1)( 4i + 12)

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have to simplify (8i + 7)(9i + 10)/ (3i +1)( 4i + 12)

Now (8i + 7)(9i + 10)/ (3i +1)( 4i + 12)

open the brackets

=> (72i^2 + 63i + 80i + 70) / ( 12i^2 + 4i + 36i + 12)

substitute i^2 with -1

=>( -72 + 63i + 80i + 70) / ( -12 + 4i + 36i + 12)

=> (-2 + 143i) / 40i

=> (-2 + 143i)* i / 40*i^2

=> (-2i + 143i^2) / (-40)

=> ( - 2i – 143)/ (-40)

=> 143 / 40 + i/20

Therefore (8i + 7)(9i + 10)/ (3i +1)( 4i + 12) =

143 / 40 + i/20

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

simplify ( 8i+7) (9i + 10) / (3i + 1) ( 4i + 12).

First, let us open brackets.

==> (8*9*i^2 + 80i + 63i + 70 ) / (12i^2 + 36i + 4i + 12)

Now we will combine like terms.

==?> (72i^2 + 143i + 70)/ (12i^2 + 40i + 12)

But we know that i^2 = -1

==> ( -72 + 143i + 70i) / (-12 + 40i + 12)

==? ( -2 + 143i) / 40i)

Now we will multiply and divide by -40i

==> (-2+ 143i)* -40i / 40i*-40i

==> ( 80i - 7720i^2 / 1600

==> (7720 + 80i)/ 1600

==> (143/40) + (1/20) i