Think Twice

Algebra Level 4

Identify the correct statement :

Statement 1 : $\large (-1)^{\frac{3}{2}} = \iota$

Statement 2 : $\large (-1)^{\frac{3}{2}} = -\iota$

Details:

Both the statements are correct Statement 1 only Statement 2 only Both the statements are incorrect

1 solution

Akhil Bansal
Oct 19, 2015

Statement 1 : $\Rightarrow \large (-1)^{\frac{3}{2}} =\{(-1)^3\}^{\frac{1}{2}} = (-1)^{\frac{1}{2}} = \iota$

Statement 2 : $\Rightarrow\large (-1)^{\frac{3}{2}} = \{(-1)^{\frac{1}{2}}\}^3 = \iota^3 = -\iota$

$\therefore \large (-1)^{\frac{3}{2}} = \pm\iota$