# How do you simplify (4-6i)(2+3i)?

Nov 20, 2015

$\left(4 - 6 i\right) \left(2 + 3 i\right) = 26$

#### Explanation:

{: (xx,color(white)("X")"|",4,-6i,), ("----",,"----","----",), (color(white)("X")2,color(white)("X")"|",color(white)("X")color(red)(8),color(green)(-12i),), (+3i,color(white)("X")"|",color(green)(12i),color(blue)(+18),), ("----",,"----","----",), (color(red)(8),color(green)(+0i),color(blue)(+18),,=26) :}

Nov 20, 2015

26

#### Explanation:

Given: $\left(4 - 6 i\right) \textcolor{b r o w n}{\left(3 + 3 i\right)}$

$4 \textcolor{b r o w n}{\left(2 + 3 i\right)} - 6 i \textcolor{b r o w n}{\left(2 + 3 i\right)}$...........................(1)

$\left(8 + 12 i\right) + \left(- 12 i - 18 {\left(i\right)}^{2}\right)$...................(2)

Consider $18 {i}^{2}$

${i}^{2} = - 1$

So $18 {i}^{2} = - 18$

Thus $- 18 {i}^{2} = - \left(- 18\right) = + 18$....................(3)

Substitute (3) into (2) giving

$\left(8 + 12 i\right) + \left(- 12 i + 18\right)$

$8 + \left(12 i - 12 i\right) + 18$

$8 + 0 + 18 = 26$