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NDA2023MathematicsComplex NumberActual

If is a non-real cube root of 1 , then what is the value of | 1- + ^2 | ?

Options

  1. A3
  2. B2
  3. C1
  4. D4 3

Correct answer

A. 3

Step-by-step solution

| 1-w w+w^2 |= | 1-w -1 |=|w-1| [ 1+w+w^2=0 ]= | -1+ 3 i 2 -1 |= | -1+ 3 i-2 2 |= | -3 2 + 3 2 i |= ( -3 2 )^2+ ( 3 2 )^2 = 9 4 + 3 4 = 3

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