Question

What the value of omega in mathamatics?

Answer 1

Unity or 11 has three cube roots: ww and w2w2, the imaginary cube roots, and 11, the real cube root.

The numeric value of ww and w2w2 can be obtained in the following manner:

LetLet x=1x=1

⇒x3=1⇒x3=1

⇒x3−1=0⇒x3−1=0

⇒(x−1)(x2+x+1)=0⇒(x−1)(x2+x+1)=0 [Using the formula: a3−b3=(a−b)(a2+ab+b2)a3−b3=(a−b)(a2+ab+b2)]

⇒x−1=0⇒x−1=0 oror x2+x+1=0x2+x+1=0

Hence, two cases arise:

CASE I:

x=1x=1

CASE II:

x=−1±12−4(1)1√2.1x=−1±12−4(1)12.1 [Using Sridharacharya’s formula for solving a quadratic equation]

⇒x=−1±−3√2⇒x=−1±−32

⇒x=−1±3√i2⇒x=−1±3i2

These values of xx are the values of ww and w2w2.