TUTORIALS:

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
