Question 380075
Additive inverses for complex numbers are just like they are for real numbers: they mean the number you'd add to get back to 0.  Just like real numbers, this means that you change the signs.  Thus, the additive inverse of -4+7i is 4-7i

The absolute value is the distance from zero in the complex plane, which means we basically use the distance formula: {{{sqrt(x^2+y^2)}}} where x is the real part and y is the imaginary part.  |1 - 4i| = {{{sqrt((1)^2+(-4)^2)}}} = {{{sqrt(1+16)}}} = {{{sqrt(17)}}}