Answer:
-34 + 13i
Explanation:
to solve (-2 + 7i)(3+4i), we can use FOIL which is:
First
Outside
Inside
Last
lets start off with F, we multiply the first 2 terms of each expression
(-2 + 7i)(3+4i)
this gives us -6
next is O, we multiply the 2 outside times of the expression:
(-2 + 7i)(3+4i)
this gives us -8i
I is the next step, we multiply the 2 terms on the inside:
(-2 + 7i)(3+4i)
this gives us 21i
the last step is the letter L in which we multiply the last terms of each expression:
(-2 + 7i)(3+4i)
this gives us -28, and the reason for that is because if we multiply 7i × 4i gives us 28i². i² is equal to -1, so we multiply 28 by -1 which gives us -28
so this gives us the new expression:
-6 -8i + 21i - 28
we now combine like terms which gives us the expression
-34 + 13i
this cannot be simplified any further, so this is our answer in standard form