The teacher will be very surprised to see your correct solution 😉
x1 = 1
x2 = 2
/ / / ___\\\ / / ___\\ | 4 _____ |atan\17*\/ 3 /|| 4 _____ |atan\17*\/ 3 /| | ___ \/ 217 *cos|--------------|| \/ 217 *sin|--------------| 3 | 3*\/ 3 \ 2 /| \ 2 / x3 = - - + I*|- ------- + ---------------------------| + --------------------------- 4 \ 4 2 / 2
/ / / ___\\\ / / ___\\ | 4 _____ |atan\17*\/ 3 /|| 4 _____ |atan\17*\/ 3 /| | ___ \/ 217 *cos|--------------|| \/ 217 *sin|--------------| 3 |3*\/ 3 \ 2 /| \ 2 / x4 = - - + I*|------- + ---------------------------| - --------------------------- 4 \ 4 2 / 2
/ / / ___\\\ / / ___\\ | 4 _____ |atan\17*\/ 3 /|| 4 _____ |atan\17*\/ 3 /| | ___ \/ 217 *cos|--------------|| \/ 217 *sin|--------------| 3 |3*\/ 3 \ 2 /| \ 2 / x5 = - - + I*|------- - ---------------------------| + --------------------------- 4 \ 4 2 / 2
/ / / ___\\\ / / ___\\ | 4 _____ |atan\17*\/ 3 /|| 4 _____ |atan\17*\/ 3 /| | ___ \/ 217 *cos|--------------|| \/ 217 *sin|--------------| 3 | 3*\/ 3 \ 2 /| \ 2 / x6 = - - + I*|- ------- - ---------------------------| - --------------------------- 4 \ 4 2 / 2
x6 = -217^(1/4)*sin(atan(17*sqrt(3))/2)/2 - 3/4 + i*(-217^(1/4)*cos(atan(17*sqrt(3))/2)/2 - 3*sqrt(3)/4)
sum
/ / / ___\\\ / / ___\\ / / / ___\\\ / / ___\\ / / / ___\\\ / / ___\\ / / / ___\\\ / / ___\\ | 4 _____ |atan\17*\/ 3 /|| 4 _____ |atan\17*\/ 3 /| | 4 _____ |atan\17*\/ 3 /|| 4 _____ |atan\17*\/ 3 /| | 4 _____ |atan\17*\/ 3 /|| 4 _____ |atan\17*\/ 3 /| | 4 _____ |atan\17*\/ 3 /|| 4 _____ |atan\17*\/ 3 /| | ___ \/ 217 *cos|--------------|| \/ 217 *sin|--------------| | ___ \/ 217 *cos|--------------|| \/ 217 *sin|--------------| | ___ \/ 217 *cos|--------------|| \/ 217 *sin|--------------| | ___ \/ 217 *cos|--------------|| \/ 217 *sin|--------------| 3 | 3*\/ 3 \ 2 /| \ 2 / 3 |3*\/ 3 \ 2 /| \ 2 / 3 |3*\/ 3 \ 2 /| \ 2 / 3 | 3*\/ 3 \ 2 /| \ 2 / 1 + 2 + - - + I*|- ------- + ---------------------------| + --------------------------- + - - + I*|------- + ---------------------------| - --------------------------- + - - + I*|------- - ---------------------------| + --------------------------- + - - + I*|- ------- - ---------------------------| - --------------------------- 4 \ 4 2 / 2 4 \ 4 2 / 2 4 \ 4 2 / 2 4 \ 4 2 / 2
=
/ / / ___\\\ / / / ___\\\ / / / ___\\\ / / / ___\\\ | 4 _____ |atan\17*\/ 3 /|| | 4 _____ |atan\17*\/ 3 /|| | 4 _____ |atan\17*\/ 3 /|| | 4 _____ |atan\17*\/ 3 /|| | ___ \/ 217 *cos|--------------|| | ___ \/ 217 *cos|--------------|| | ___ \/ 217 *cos|--------------|| | ___ \/ 217 *cos|--------------|| | 3*\/ 3 \ 2 /| | 3*\/ 3 \ 2 /| |3*\/ 3 \ 2 /| |3*\/ 3 \ 2 /| I*|- ------- + ---------------------------| + I*|- ------- - ---------------------------| + I*|------- + ---------------------------| + I*|------- - ---------------------------| \ 4 2 / \ 4 2 / \ 4 2 / \ 4 2 /
product
/ / / / ___\\\ / / ___\\\ / / / / ___\\\ / / ___\\\ / / / / ___\\\ / / ___\\\ / / / / ___\\\ / / ___\\\ | | 4 _____ |atan\17*\/ 3 /|| 4 _____ |atan\17*\/ 3 /|| | | 4 _____ |atan\17*\/ 3 /|| 4 _____ |atan\17*\/ 3 /|| | | 4 _____ |atan\17*\/ 3 /|| 4 _____ |atan\17*\/ 3 /|| | | 4 _____ |atan\17*\/ 3 /|| 4 _____ |atan\17*\/ 3 /|| | | ___ \/ 217 *cos|--------------|| \/ 217 *sin|--------------|| | | ___ \/ 217 *cos|--------------|| \/ 217 *sin|--------------|| | | ___ \/ 217 *cos|--------------|| \/ 217 *sin|--------------|| | | ___ \/ 217 *cos|--------------|| \/ 217 *sin|--------------|| | 3 | 3*\/ 3 \ 2 /| \ 2 /| | 3 |3*\/ 3 \ 2 /| \ 2 /| | 3 |3*\/ 3 \ 2 /| \ 2 /| | 3 | 3*\/ 3 \ 2 /| \ 2 /| 2*|- - + I*|- ------- + ---------------------------| + ---------------------------|*|- - + I*|------- + ---------------------------| - ---------------------------|*|- - + I*|------- - ---------------------------| + ---------------------------|*|- - + I*|- ------- - ---------------------------| - ---------------------------| \ 4 \ 4 2 / 2 / \ 4 \ 4 2 / 2 / \ 4 \ 4 2 / 2 / \ 4 \ 4 2 / 2 /
=
8
8
x1 = 2.0
x2 = 0.583740972914917 - 0.0807680339067363*i
x3 = 0.583740972914917 + 0.0807680339067363*i
x4 = -2.08374097291492 - 2.67884424526005*i
x5 = 1.0
x6 = -2.08374097291492 + 2.67884424526005*i
x6 = -2.08374097291492 + 2.67884424526005*i