Question

The method used to divide complex numbers is similar to the method used to divide radical expressions. Explain why. Give an example.

Answer 1

Hello - what do you know about the similarities between complex numbers and radical expressions?

Answer 2

that they are treated the same when solving

Answer 3

i think

Answer 4

Can you give me an example of a complex number?

Answer 5

Not doing anything with it, just one unto itself.

Answer 6

\[\sqrt{-2} = 2i\]

Answer 7

or i guess \[i \sqrt{2}\]

Answer 8

That's the imaginary part of a complex number, and yeah, your second one is right.

\[ 0+ i\sqrt 2\]

What do you notice about the "i"? Might it be a radical? ^_^

Answer 9

So given the complex number 12+6i, if you divide it by 2i

\[\frac{12+6i}{2i}=?\]

Answer 10

You get

\[ \frac{12}{2i}+\frac{6i}{2i} = ?\]

What does the second term turn into?

Answer 11

\[\frac{6}{2} \cdot \cancel{\frac{i}{i}}^1 = ?\]

Answer 12

For the second expression, the i's cancel out nd leave you with real number. htat's boring though!

Looking at the first term

\[\frac{12}{2} \cdot \frac{1}{i} = \frac{12}{2} \cdot \frac{1}{\sqrt{-1}}\]

And since you have the "i" on the bottom, you have a radical on the bottom - can you rationalize a term with a radical in the denominator?