Question 993057
1+2i/ 1- square root of -64
<pre>
{{{(1+2i)/(1-sqrt(-64))}}}

Change {{{sqrt(-64)}}} to {{{sqrt(-1*64)}}} to {{{sqrt(-1)*sqrt(64)}}} to {{{i*8}}} to {{{8i}}}

{{{(1+2i)/(1-8i)}}}

Multiply by the conjugate of the denominator over itself {{{(1+8i)/(1+8i)}}}
which we can do because that is just multiplying by 1.

{{{((1+2i)(1+8i))/((1-8i)(1+8i))}}}

Use FOIL on top and bottom:

{{{(1+8i+2i+16i^2)/(1+8i-8i-64i^2)}}}

Combine like terms and eliminate terms that have 0 sum:

{{{(1+10i+16i^2)/(1-64i^2)}}}

Substitute -1 for i<sup>2</sup>

{{{(1+10i+16(-1))/(1-64(-1))}}}

{{{(1+10i-16)/(1+64)}}}

Combine like terms:

{{{(-15+10i)/65}}}

To express in terms of a+bi, break into two fractions:

{{{-15/65+10i/65}}}

Reduce the fractions:

{{{-3/13+2i/13}}}

Move the i factor in the second term from the numerator
to the right:

{{{-3/13+expr(2/13)i}}} 

Edwin</pre>