Question 386387



<pre>

(3 - 2i)x + 3 = (4 + 3i)x - 4i
 3x - 2ix + 3 = 4x + 3ix - 4i

3x - 2ix - 4x - 3ix = -3 - 4i

          -x - 5ix = -3 - 4i

        x(-1 - 5i) = -3 - 4i

                  x = {{{(-3-4i)/(-1-5i)}}}

Multiply by the conjugate of the denominator over itself:

                  x = {{{(-3-4i)/(-1-5i)}}}{{{(-1+5i)/(-1+5i)}}}

                  x = {{{(3-15i+4i-20i^2)/(1-5i+5i-25i^2)}}}

                  x = {{{(3-11i-20i^2)/(1-25i^2)}}}

Replace iČ by -1

                  x = {{{(3-11i-20(-1))/(1-25(-1))}}}

                  x = {{{3-11i+20)/(1+25)}}}

                  x = {{{23-11i)/26}}}

                  x = {{{23/26-expr(11/26)i}}} 
                  
Checking:

{{{(3 - 2i)x + 3 = (4 + 3i)x - 4i}}}
{{{(3 - 2i)(23/26-expr(11/26)i) + 3 = (4 + 3i)(23/26-expr(11/26)i) - 4i}}}
{{{69/26-expr(33/26)i-expr(46/26)i +expr(22/26)i^2 + 3=92/26-expr(44/26)i+expr(69/26)i-expr(33/26)i^2-4i}}}

{{{69/26-expr(79/26)i +expr(22/26)i^2 + 3=92/26+expr(25/26)i-expr(33/26)i^2-4i}}}

Change iČ to -1

{{{69/26-expr(79/26)i +expr(22/26)(-1) + 3=92/26+expr(25/26)i-expr(33/26)(-1)-4i}}}

{{{47/26-expr(79/26)i + 3=125/26+expr(25/26)i-4i}}}

Write 3 as {{{78/26}}} and -4i as {{{-expr(104/26)i}}}

{{{47/26-expr(79/26)i + 78/26=125/26+expr(25/26)i-expr(104/26)i}}}

{{{125/26-expr(79/26)i = 125/26-expr(79/26)i}}}