Question

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

Answer 1

`(4-6i)(2+3i)= 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) :}`

Answer 2

26

Explanation:

Given: `(4-6i)color(brown)((3+3i))`

`4color(brown)((2+3i)) -6icolor(brown)((2+3i))`...........................(1)

`(8+12i) + (-12i-18(i)^2)`...................(2)

Consider `18i^2`

`i^2 =-1`

So `18i^2= -18`

Thus `-18i^2= -(-18)=+18`....................(3)

Substitute (3) into (2) giving

`(8+12i)+(-12i +18)`

`8 +(12i -12i) + 18`

`8+0+18 = 26`