Let ω be a complex number such that 2 ω + 1 = z where z = - 3 . If 1 1 1 1 - ω 2 - 1 ω 2 1 ω 2 ω 7 = 3 k , Then k can be equal to:

Question

Let &#969; be a complex number such that 2 &#969; + 1 = z where z = - 3 . If 1 1 1 1 - &#969; 2 - 1 &#969; 2 1 &#969; 2 &#969; 7 = 3 k , Then k can be equal to:

Aicharya · Accepted Answer

&#969; = &#160; - 1 2 + 3 2 &#160; i (cube root of unity) So, 1 + &#969; + &#969; 2 = 0 and &#969; 3 =1 Now 1 1 1 1 &#969; &#969; 2 1 &#969; 2 &#969; = 3 &#969; 2 - &#969; So k = &#969; 2 - &#969; &#8658; k = - 1 2 - 3 2 i - - 1 2 + 3 2 i &#8658; k = - 3 i &#8658; k = - z

Let ω be a complex number such that 2 ω + 1 = z where z = - 3 . If 1 1 1 1 - ω 2 - 1 ω 2…

Solution

Let &#969; be a complex number such that 2 &#969; + 1 = z where z = - 3 . If 1 1 1 1 - &#969; 2 - 1 &#969; 2…

Solution

Let ω be a complex number such that 2 ω + 1 = z where z = - 3 . If 1 1 1 1 - ω 2 - 1 ω 2…