SOLUTION: True of false? The number (1/2)i is the reciprocal of 2i. Could you please provide a detailed explanation on how you achieved you answer, and show me how the product of 2i

Question 189013: True of false?
The number (1/2)i is the reciprocal of 2i.

Could you please provide a detailed explanation on how you achieved you answer, and show me how the product of 2i and its reciprocal equal 1.
Found 2 solutions by jim_thompson5910, Mathtut:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let

The reciprocal of "x" is simply

Plug in

So the reciprocal of is (not )

So the statement is false.

Now multiply by its reciprocal

Combine the fractions.

Cancel out the common terms.

Simplify

Multiply EVERY term by "i" to make the denominator real (this doesn't change the expression)

Multiply

Replace with

Note: . So

Reduce

So
Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
recipricals of a given number say a take the form of 1/a
:
the recriprical of a would be 1/a
:
so the reciprical of 2i is 1/2i.......which is not the same as (1/2)i....therefore the statement is false
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