We shall now derive a formula for taking the square root of a complex number. Assuming that it, too, is a complex number,
Using the quadratic formula,
For the formula, I am changing every “±” to “+”, as any use of “-” in those locations leads to the same square root, the negative root or an extraneous root.
Formula for the Square Root of a Complex Number:
Or, instead of independently calculating the denominator of the coefficient of i, merely replace it with twice the real term of the square root you are finding, as you have already found that real term.
In both examples, you could ignore the denominator of the coefficient of i until you’ve determined the real term of your answer, and then just insert twice that term for the unwritten denominator (4 in the first example, 6 in the second). I leave it to the reader to confirm these results.
TO BE CONTINUED