### Concept (1)

Fractions with negative roots in the denominator or with i in the denominator must be rationalized (since i represents a square root). When dividing complex numbers with negative roots, simplify in terms of imaginary numbers and then multiply the numerator and denominator by i. When a binomial is in the denominator, rewrite using i and then multiply the numerator and denominator by the conjugate.

### Sample Problems (7)

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Simplify:

20
-72
###### Problem 1
How to rationalize the denominator when dealing with an imaginary number.

Simplify:

-1 + √-4
4 + √-9
###### Problem 2
How to rationalize the denominator when dealing with a complex number.
###### Problem 3
How to divide by an imaginary monomial.
###### Problem 4
How to simplify radical quotients with a negative root in the denominator.
###### Problem 5
Dividing complex numbers where the denominator contains an imaginary number.
###### Problem 6
How to divide complex numbers.
###### Problem 7
Rationalizing denominators where there is a root of a negative number, meaning we'll likely have an imaginary result.