Question 1206982
<pre>

Here's another way to do this problem:

Assume

{{{a+bi}}}{{{""=""}}}{{{sqrt(-10i)}}}, where a and b are real numbers.

{{{a^2+2a*b*i+b^2*i^2}}}{{{""=""}}}{{{-10i}}}

{{{a^2+2a*b*i+b^2*(-1)}}}{{{""=""}}}{{{-10i}}}

{{{a^2+2a*b*i-b^2}}}{{{""=""}}}{{{-10i}}}

Set real parts on the left and right equal, and same with imaginary parts:

{{{system(a^2-b^2=0,2ab=-10)}}}

{{{system(a^2=b^2,ab=-5)}}}

{{{system(a="" +- b,ab=-5)}}}

ab=-5 tells us that a and b have opposite signs, thus a=-b

{{{a^2=b^2}}}
{{{a=sqrt(5)}}} and {{{b=-sqrt(5)}}}
or
{{{a=-sqrt(5)}}} and {{{b=sqrt(5)}}}

Thus the answers are

{{{sqrt(5)-i*sqrt(5)}}} and {{{-sqrt(5) + i*sqrt(5)}}}

Edwin</pre>