Astand-up comedian uses algebra in some jokes, including one about a telephone recording that announces "you have just reached a pure imaginary number. multiply by i and dial again." explain the joke.

When we work with imaginary numbers, we have that

i = √(-1)

then, we have that i*i = √(-1)*√(-1) = -1

An imaginary number is a number of form A + B*i, where A and B are real numbers.

Now, a purely imaginary number is a number of the form B*i, where B is a real number.

Then, if we multiply this number by i, we have that:

B*i*i = B*(-1) = -B

now we have a real number.

The joke is that now you can "reach" a real number.

the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

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