Question

Multiply these complex numbers

(7-3i) (2-i)

Please show the steps

Answer 1

well... what do you get?

Answer 2

is just a pretty straightforward FOIL or just plain multiplication

Answer 3

i way off, i get 17+i

Answer 4

\(\bf \color{blue}{7-3i}) (2-i)\implies \color{blue}{7}\cdot (2-i)+(\color{blue}{-3i}\cdot (2-i)\)

Answer 5

what does that give you?

Answer 6

14-i-6i-i ?

Answer 7

hmmm you need to DISTRIBUTE the 7 to both terms inside the parenthesis

Answer 8

14 -7i -6i^2

Answer 9

\(\bf (7-3i) (2-i)\implies 7\cdot (2-i)+(-3i\cdot (2-i)\\ \quad \\
(7\cdot 2)+(7\cdot -i)+(-3i\cdot 2)+(-3i\cdot -i)
\)

Answer 10

wouldn't i x i equal i^2 ?

Answer 11

yes

Answer 12

so how would i do that with -i ?

Answer 13

\(\bf (7-3i) (2-i)\implies 7\cdot (2-i)+(-3i\cdot (2-i)\\ \quad \\
(7\cdot 2)+(7\cdot -i)+(-3i\cdot 2)+(-3i\cdot -i)\\ \quad \\
14-7i-6i+3i^2\\ \quad \\
\textit{recall that}\\ \quad \\
\color{blue}{i^2=\sqrt{-1}\cdot \sqrt{-1}\implies (\sqrt{-1})^2\implies \sqrt{(-1)^2}\implies -1}\qquad thus\\ \quad \\
14-7i-6i+3i^2\implies 14-7i-6i+3(-1)\implies 14-7i-6i-3\\ \quad \\
11-13i\)

Answer 14

i got everything up to the -3, for some reason i keep getting positive 3

Answer 15

- times + = -
- times - = +

same signs multiplication gives POSITIVE
different signs multiplication gives NEGATIVE

+3 * -1 = -3