Question

If (1 + ω²)^m = (1 + ω⁴)^m and ω is an imaginary cube root of unity, then least positive integral value of m is ______.

Options

• 6

• 5

• 4

• 3

Answer 1

If (1 + ω²)^m = (1 + ω⁴)^m and ω is an imaginary cube root of unity, then least positive integral value of m is 3.

Explanation:

We have,

(1 + ω²)^m = (1 + ω⁴)^m   ......[∵ ω² = 1]

⇒ (1 + ω²)^m = (1 + ω)^m

⇒ (– ω²)^m = (– ω²)^m 

⇒ `(ω/ω^2)^"m"` = 1

⇒ (ω)^m = 1 = (ω³)

Hence, least positive integral value of m is 3.