This is copied from Paul's online math notes There is one final topic that we need to touch on before leaving this section. As we noted back in the section on radicals even though √9=3 there are in fact two numbers that we can square to get 9. We can square both 3 and -3. The same will hold for square roots of negative numbers. As we saw earlier √-9=3i . As with square roots of positive numbers in this case we are really asking what did we square to get -9? Well it’s easy enough to check that 3i is correct. (3i)2=9i2= -9 However, that is not the only possibility. Consider the following, (-3i)2=(-3)2i2=9i2= -9 and so if we square -3i we will also get -9. So, when taking the square root of a negative number there are really two numbers that we can square to get the number under the radical. However, we will ALWAYS take the positive number for the value of the square root just as we do with the square root of positive numbers. Why do we do so with complex numbers and radicals?