Imaginary Numbers
To find a product such as
 begin by rewriting each square
root in terms of i.
Example
Simplify:
| Solution |
|
Rewrite each square root using
 |
 |
| Simplify each square root.
Multiply.
Use i2 = -1.
Multiply.
Thus,
 |
= 3 · i · 4 · i
= 12 · i2
= 12 · (-1)
= -12 |
Note:
Be careful! The Multiplication Property of
Square Roots,
 does not apply if a or b is negative.
If the radicand of a square root contains a
negative number, be sure to write the
square root in terms of i before you
simplify.
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