How do you simplify (2-i)(3+2i)(1-4i)?

Jul 21, 2018

$\textcolor{c y a n}{\implies 12 - 31 i}$

Explanation:

Here are the steps required for Multiplying Complex Numbers:

color(brown)("Step 1: Distribute (or FOIL) to remove the parenthesis."

color(purple)("Step 2 : Simplify the powers of i, specifically remember that i2 = –1."
color(gray)("Step 3 : Combine like terms, that is, combine real numbers with real numbers and imaginary numbers with imaginary numbers."

$\text{Given : } \left(2 - i\right) \cdot \left(3 + 2 i\right) \cdot \left(1 - 4 i\right)$

$\implies \left(6 + 4 i - 3 i - 2 {i}^{2}\right) \cdot \left(1 - 4 i\right)$

$\implies \left(6 + 4 i - 3 i + 2\right) \cdot \left(1 - 4 i\right)$

$\implies \left(8 + i\right) \cdot \left(1 - 4 i\right)$

$\implies 8 - 32 i + 1 i - 4 {i}^{2}$

$\implies 8 - 32 i + i + 4$

$\textcolor{c y a n}{\implies 12 - 31 i}$