question_answer

\[{{\left( -64 \right)}^{1/4}}\] is equal to-

A) \[\pm \,2\left( 1+i \right)\]       

B)        \[\pm \,2\left( 1-i \right)\]

C) \[\pm 2\left( 1\pm i \right)\]        

D)        None of these

Correct Answer: C

Solution :

[c] \[{{\left( -64 \right)}^{1/4}}={{2}^{3/2}}{{\left( -1 \right)}^{1/4}}\] roots \[\Rightarrow \text{ }2\left( 1\pm 1 \right),2\left( -1\pm 1 \right)\]