Question

(5+2i)(4+3i)
Can someone please explain me in steps how to simplify it?

Answer 1

you have a choice here
you can either just multiply out like in "foil" (ugh) or you can use a formula for multiplying complex numbers. which do you choose (or both)?

Answer 2

\[(a+bi)(c+di)=(ac-bd)+(ad+bc)i\] you should really learn this if you are going to see these more often.

Answer 3

The one you may think is easier, it seems the foil method isn't your choice anyway. lol

Answer 4

so in your case you will get
\[(5+2i)(4+3i)=(5\times 4-2\times 3)+(5\times 3+2\times 4)i\]
\[(20-6)+(15+8)i\]
\[14+23i\]

Answer 5

(5+2i)(4+3i)
(2i)(3i)=6i^2=-6
(2i)(4)=8i
(3i)(5)=15i
(4)(5)=20

14+23i

Answer 6

if this is too hard to remember multiply out like you would a two term by two term polynomial, and then at the end recall that
\[i^2=-1\] so you can put
\[5\times 4+5\times 3i+2\times 4i+6\times i^2\]
\[20+15i+8i-6\]
\[14+23i\] it is your choice

Answer 7

Thanks that formula was really helpful. :)