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

2 Answers
Alan P.
Nov 20, 2015

#(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) :}#

Tony B
Nov 20, 2015

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#

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