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Chapter 2: Problem 68

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

Short Answer

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

Step by step solution

01

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.
02

Simplify

After plugging in our standard values, we simplify the equation further. So our equation \(4(-1) - 2(-i)\) becomes \(-4 + 2i\).
03

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.

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Most popular questions from this chapter

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