Problem 68 - Algebra and Trigonometry Real Mathematics, Real People

Question

Simplify the complex number and write it in standard form. $$4 i^{2}-2 i^{3}$$

Step-by-Step Solution

Answer

So the complex number \(4 i^{2}-2 i^{3}\) in standard form is \(-4 + 2i\).

Step 1: Apply the standard values

First, we have to apply the standard values for \(i^{2}\) and \(i^{3}\). And our standard values are \(i^{2}\) = -1 and \(i^{3}\) = -\(i\). So we plug these values into the equation: \(4 i^{2}-2 i^{3}\) becomes \(4(-1) - 2(-i)\) following substitution.

Step 2: Simplify

After plugging in our standard values, we simplify the equation further. So our equation \(4(-1) - 2(-i)\) becomes \(-4 + 2i\).

Step 3: Write in standard form

The standard form of a complex number is \(a+bi\) where \(a\) is the real part and \(b\) is the imaginary part. The simplified result \(-4 + 2i\) is already in this standard form, so no additional changes are required.