Question 189013
Let {{{x=2i}}}



The reciprocal of "x" is simply {{{1/x}}}



{{{1/(2i)}}} Plug in {{{x=2i}}}



So the reciprocal of {{{2i}}} is {{{1/(2i)}}} (not {{{(1/2)i}}})



So the statement is false.



Now multiply {{{2i}}} by its reciprocal {{{1/(2i)}}}



{{{(2i)(1/(2i))}}}



{{{(2i)/(2i)}}} Combine the fractions.



{{{(cross(2)i)/(cross(2)i)}}} Cancel out the common terms.



{{{i/i}}} Simplify



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



{{{(i^2)/(i^2)}}} Multiply



{{{(-1)/(-1)}}} Replace {{{i^2}}} with {{{-1}}}



Note: {{{i=sqrt(-1)}}}. So {{{i^2=(sqrt(-1))^2=-1}}}



{{{1}}} Reduce



So {{{(2i)(1/(2i))=1}}}