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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 