Simplify x^2 + 16 = 0 using i

Step by step

The question

Question: solve x² + 16 = 0 using i.

No real number times itself is negative.

So we use a new number: i, the square root of minus 1.

So i squared is minus 1.

1 Get x² alone

The + 16 is in the way.

To remove + 16, we take away 16.

We do it on both sides, so they stay equal.

+ 16 and − 16 make zero.

Cross them out.

0 minus 16 is −16.

Before i, we could not solve this.

Now it has two answers.

2 Square root of both sides

Something squared is minus 16.

So that something is the square root of minus 16, or minus it.

Both work, because minus times minus is plus.

So x is the square root of minus 16, or minus it.

√(−16) is √16 times √(−1): 4 times i.

So x = 4i or x = −4i.

3 Check

Let's check 4i.

(4i)² is 16 times i², that is −16.

We get 0.

Now −4i.

We get 0 again.

Both answers work!

Let's look back.

First: get x² alone.

Then: square root of both sides.

Last: check.