Question

Find the product: (2-6i)(7-5i)

Answer 1

I know the answer is 16-52i,but have no idea why

Answer 2

I originally got 14-52i

Answer 3

*the answer is -16-52i

Answer 4

But I want to know why

Answer 5

\(\bf (2-6i)(7-5i) \implies 14-10i-42i+30i^2\\ \quad \\ \quad \\
14+30i^2-52i\\
\textit{keep in mind that } i^2 = \sqrt{ (-1)}\times \sqrt{ (-1)} \implies \sqrt{ (-1)^2} \implies -1\)

Answer 6

I still don't understand why that would equal -16-52i

Answer 7

\(\bf (2-6i)(7-5i) \implies 14-10i-42i+30i^2\\ \quad \\ \quad \\
14+30i^2-52i \\
\textit{keep in mind that } i^2 = \sqrt{ (-1)}\times \sqrt{ (-1)} \implies \sqrt{ (-1)^2} \implies -1\\\quad \\
14+30i^2-52i \implies 14+30(-1)-52i \)

Answer 8

see it now?

Answer 9

\(\bf 14+30i^2-52i \implies 14+30(-1)-52i \implies 14-30-52i\)

Answer 10

yes. Thank you. Not to bother you, but if we have (-6+i)(-6-i), why would that equal 37 rather than 37+6i?

Answer 11

\(\bf (-6+i)(-6-i) \implies 36\cancel{+6i}\cancel{-6i}-i^2 \implies 36-i^2\\
\textit{keep in mind that } i^2 = \sqrt{ (-1)}\times \sqrt{ (-1)} \implies \sqrt{ (-1)^2} \implies -1\\ \quad \\ \quad \\
36-i^2 \implies 36-(-1) \implies 37\)

Answer 12

But I FOILd it and got 36+6i+1 and that's why I have 37+6i rather than just 37.

Answer 13

\(\bf (-6+i)(-6-i) \\ \quad \\ \quad \\
-6 \times -6 = 6\\
-6 \times -i = 6i\\ \quad \\ \quad \\
+i \times -6 = -6i\\
+i \times -i = -i^2\)

Answer 14

woops.... darn... got a typo...

Answer 15

\(\bf (-6+i)(-6-i) \\ \quad \\ \quad \\
-6 \times -6 = 6^2\\
-6 \times -i = 6i\\ \quad \\ \quad \\
+i \times -6 = -6i\\
+i \times -i = -i^2\)

Answer 16

in FOIL it should give you the same values anyhow