Question

Can someone simplify this completely? show steps please?
(√2- 4i)(√2 +4i)

Answer 1

(A+B)(A-B)=A^2-B^2
so we have
\[(\sqrt{2}-4i)(\sqrt{2}+4i)=(\sqrt{2})^2-(4i)^2\]

Answer 2

\[=2-4^2i^2=2-(16)(-1)=2+16=18\]

Answer 3

just foil. multiple first set of numbers sqrt2* sqrt2=2
then outer numbers sqrt2*4i =4isqrt2
then inner number qrt2*4i =4isqrt2
then last 4i*4i=16 i
then answer is =2+4i*sqrt2-41*sqrt2-16i
which when simplified = 2+16i

i think.....

Answer 4

wait actually it'll be 2+16(i^2) = 2+16 = 18

Answer 5

aaaaaaaaaaaaaaaaarghhhhhhhhhhhhhhhhh

Answer 6

\[(a+bi)(a-bi)=a^2+b^2\] finished

Answer 7

\[\sqrt{2}^2=2\]
\[4^2=16\]
\[2+16=18\]

Answer 8

thank you everyone. my book has no example and my teacher isn't that good at explaining.

Answer 9

forget the "foil" and forget the flippin' "i"just know that a complex number multiplied by its complex conjugate is the sum of the squares

Answer 10

but it's important that she does it the way she is learning in school, even if it's the longer... more complicated way... which can suck