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

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> 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       Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=2i


The reciprocal of "x" is simply 1%2Fx


1%2F%282i%29 Plug in x=2i


So the reciprocal of 2i is 1%2F%282i%29 (not %281%2F2%29i)


So the statement is false.


Now multiply 2i by its reciprocal 1%2F%282i%29


%282i%29%281%2F%282i%29%29


%282i%29%2F%282i%29 Combine the fractions.


%28cross%282%29i%29%2F%28cross%282%29i%29 Cancel out the common terms.


i%2Fi Simplify


%28i%2Ai%29%2F%28i%2Ai%29 Multiply EVERY term by "i" to make the denominator real (this doesn't change the expression)


%28i%5E2%29%2F%28i%5E2%29 Multiply


%28-1%29%2F%28-1%29 Replace i%5E2 with -1


Note: i=sqrt%28-1%29. So i%5E2=%28sqrt%28-1%29%29%5E2=-1


1 Reduce


So %282i%29%281%2F%282i%29%29=1

Answer by Mathtut(3670) About Me  (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