Question 694095
you have to know that 
{{{ i = sqrt(-1) }}}
{{{ i^2 = -1}}}
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{{{ i^3 = i*(-1) }}}
{{{ i^3 = -i }}}
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{{{ i^4 = (-1)*(-1) }}}
{{{ i^4 = 1 }}}
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To multiply {{{ 6 - 5i )*( 4 - 9i ) }}}, you need
to know the more basic operation
{{{ ( a + b )*( c + d ) = a*c + b*c + a*d + b*d }}}
You're doing the same thing with operations on {{{ i }}}
 {{{ 6 - 5i )*( 4 - 9i ) = 24 - 20i - 54i + 45*i^2 }}}
 {{{ 6 - 5i )*( 4 - 9i ) = 24 + 45*(-1)  - 20i - 54i }}}
 {{{ 6 - 5i )*( 4 - 9i ) = -21  - 74i }}}
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{{{ ( 2 + 3*i ) / ( 4 - 5*i ) }}}
Multiply top and bottom by {{{ 4 + 5*i }}}
{{{ ( ( 2 + 3*i ) / ( 4 - 5*i ) )*( ( 4 + 5i ) / ( 4 + 5*i ) ) }}}
{{{ ( ( 2 + 3*I )*( 4 + 5*i ) ) / ( ( 4 - 5*i )*( 4 + 5*i ) ) }}}
{{{ ( ( 2 + 3*I )*( 4 + 5*i ) ) / ( 16 - 25*(i^2) ) }}}
{{{ ( 8 + 12*i + 10*i + 15*i^2 ) / ( 16 + 25 ) }}}
{{{ ( 8 - 15 + 22i ) / 41 }}}
{{{ -7/41 + (22/41)*i }}}
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It's easy to make a mistake on these, but
I hope you get the idea