Question 423401
In general the absolute value of something is it distance from zero. In the case of a complex number, a+bi, its absolute value is its distance from the zero complex number,  0+0i.<br>
If you have learned how to plot complex numbers on a coordinate system you can plot the two points and see that the distance between a+bi and 0+0i can be found with the distance formula, {{{d = sqrt((x[2] - x[1])^2 + (y[2] - y[1])^2)}}}. So
{{{abs(a+bi) = sqrt((a-0)^2 + (b-0)^2)}}}
which simplifies to:
{{{abs(a+bi) = sqrt(a^2 + b^2)}}}
Some people just memorize this formula. Others figure it out from the distance formula.<br>
Now that we have a formula for absolute value of a complex number we can use it on your complex number:
{{{abs(-1+3i) = sqrt((-1)^2 + (3)^2)}}}
which simplifies as follows:
{{{abs(-1+3i) = sqrt(1 + 9)}}}
{{{abs(-1+3i) = sqrt(10)}}}
Since {{{sqrt(10)}}} does not simplify further we are finished.