Question

find all the value of complex no roots​

Answer 1

1+i=(√2cos¼π+sin¼π)=√2e^¼πi

³√(1+i)=√2(e^¼πi+2πni)^1/3

z=↘2^(1/6)↙ , (2)^1/6(cis(±π/12)↙

cosπ/12=cos(¼π-π/6)=√2/4(√3+1)=¼(√6+√2)

sinπ/12=¼(√6-√2)

z=↘2^(1/6)↙ , 2^(1/6)*2^(-2){(√6+√2)±i(√6-√2)={(√6+√2)}+i(√6-√2)/2^(11/6)

P.S : 2^(1/6),being real,IS NOT A SOLUTION !