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TUTORIALS:
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Square Roots of Negative Complex Numbers
Note that both
(2i)2 = -4 and (-2i)2 = -4. Because the square of each of these complex numbers is
-4, both 2i and -2i are square roots of -4. We write
 . In the complex number system the square
root of any negative number is an imaginary number.
Square Root of a Negative Number
For any positive real number b,
For example,
 and
 . Note that the expression
 could easily be mistaken for the expression
, where i is under the radical.
For this reason, when the coefficient of i is a radical, we write i preceding the
radical.
Example 1
Square roots of negative numbers
Write each expression in the form a + bi, where a and b are real numbers.
Solution
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