Question 394194
1. 

{{{4i^5-6i^4+3i^3-9i^2 }}}

{{{4(i^2)(i^2)(i) - 6(i^2)(i^2) + 3(i^2)(i) - 9(i^2) }}}.........{{{(i^2)=-1}}}

{{{4(-1)(-1)(i) - 6(-1)(-1) + 3(-1)(i) - 9(-1) }}}

{{{4i - 6 - 3i + 9 }}}

{{{i + 3 }}}


2) {{{3i^4-(2i-6)-5i^2+(2+12i) }}}

{{{3(i^2)(i^2)- 2i + 6 -5i^2 +2 +12i}}}


{{{3(-1)(-1)- 2i + 6 -5(-1) + 2 +12i}}}

{{{3 - 2i + 6 +5 + 2 +12i}}}

{{{ 16 +10i }}}



3. {{{ (4i-5)*(5i-4) }}}.....multiply

{{{ ((4i)(5i) -(4i)(4) -5(5i) + 5*4)}}}

{{{ ((20i^2) -(16i) -25i + 20)}}}

{{{ ((20(-1)) -16i -25i + 20)}}}

{{{ cross(-20) -16i -25i +cross( 20))}}}

{{{ -16i -25i)}}}

{{{ -41i)}}}


4) {{{(5i+8)/(3i)}}}


{{{(5i+8)/(3i)}}}.........multiply by {{{3i}}} to eliminate {{{i}}} from denominator


{{{(5i+8)(3i)/(3i)(3i)}}}

 
{{{(5i+8)(3i)/(9i^2)}}}


{{{(15i^2+24i)/(9*-1)}}}


{{{(15(-1)+24i)/(-9)}}}


{{{(-(15-24i))/-9}}}

{{{(15-24i)/9}}}



5) {{{(11-3i)/(4+5i)}}}


{{{(11-3i)/(4+5i)}}}


{{{(11-3i)(4-5i) /(4+5i)(4-5i)}}}


{{{(44 - 55i -12i +15i^2)/(14 - 20i + 20i - 25i^2)}}}


{{{(44 - 67i +15(-1))/(14 - 25(-1))}}}


{{{(44 - 67i -15)/(14 +25)}}}


{{{(29 - 67i )/39}}}