A math student was learning about the principle square root function, and extending it to the complex numbers. For a complex number where is real and , we define .
The math student was asked to determine the value of , and wrote down the following steps. Is every step correct? If no, then what is the first incorrect step.
Step 1. Consider the complex number : Step 2. Squaring both sides, This might introduce extraneous roots.
Step 3. Simplifying the expression,
Step 7. Reject the extraneous root , and conclude that .