Question

16. Express each of the above complex numbers in the r, e form
|| 1.0, care the three cube roots of unity, prove that​

Answer 1

Answer:

Step-by-step explanation:

Then, cubing both sides we get, z3 = 1or, z3 - 1 = 0or, (z - 1)(z2 + z + 1) = 0 Therefore, either z - 1 = 0 i.e., z = 1 or, z2 + z + 1 = 0 Therefore, z = −1±12−4⋅1⋅1√2⋅1 = −1±−3√2 = -12 ± y√32 Therefore, the three cube roots of unity are1, -12 + i√32 and -12 - i√32 among them 1 is real number and the other two are conjugate complex numbers and they are also known as imaginary cube roots of unity.