Question 819959
{{{(3- sqrt(-50))/15}}}
As always, first deal with the "-" in the square root:
{{{(3- sqrt(-1*50))/15}}}
{{{(3- sqrt(-1)*sqrt(50))/15}}}
{{{(3- i*sqrt(50))/15}}}
Then simplify:
{{{(3- i*sqrt(25*2))/15}}}
{{{(3- i*sqrt(25)*sqrt(2))/15}}}
{{{(3- i*5*sqrt(2))/15}}}
or
{{{(3- 5i*sqrt(2))/15}}}
This maybe an acceptable answer.<br>
But we may want it in standard a + bi form. First we'll write the subtraction as an addition:
{{{(3+ (-5i*sqrt(2)))/15}}}
Split the fraction into two fractions:
{{{3/15+ (-5i*sqrt(2))/15}}}
Reducing the fractions:
{{{1/5+ (-i*sqrt(2))/3}}}
Factor out the "i":
{{{1/5+ (sqrt(2)/3)i}}}