Find all distinct roots real or complex of z2 32i z 2 24i

Find all distinct roots (real or complex) of z^2 + (-3-2i) z + (-2 + 24i). Enter the roots as a comma-separated list of values of the form a + bi. Use the squareroot symbol \'squareroot\" where needed to give an exact value for your answer. z =

Solution

z^2 + (-3 -2i)z + ( -2 +24i) =0

Use quadratic root formula

z = ( 3+2i +/- sqrt[ (3 +2i)^2 -4(-2+24i) ]/2

= (3 +2i +/- sqrt[9 -4 +6i +8 -96i])/2

= (3 +2i +/- sqrt(-90i +13))/2

z = ( 3 +2i + sqrt(-90i +13))/2

z = ( 3 +2i -sqrt(-90i +13))/2