How do you multiply #(-2i)^3#?

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Answer 1 · 2016-07-31T15:08:43

#8i#

First, ruse the rule that #(ab)^3=a^3*b^3#. That is:

#(-2i)^3=(-2)^3*i^3#

We can see easily that #(-2)^3=-2(-2)(-2)=-8#.

To determine the value of #i^3#, first write it as #i^2*i#. Since #i=sqrt(-1)#, we see that #i^2=(sqrt(-1))^2=-1#.

Thus, #i^3=i^2*i=-1*i=-i#.

Putting this all together, we see that:

#(-2i)^3=(-2)^3*i^3=(-8)*(-i)=8i#