Question

Simplify the following quotient of complex numbers into the form a + bi.

-9+8i / 1+2i

Answer 1

multiply top and bottom by conjugates (1-2i)

Answer 2

ohhh i learned this this year (im 14)

Answer 3

\[\frac{-9+8i}{1+2i} \cdot \frac{1-2i}{1-2i}\]

Answer 4

now remember
\[(a-b)(a+b)+a^2-b^2\]

Answer 5

how is this figured?

Answer 6

(-9 + 8i / 1 + 2i) * (1 -2i / 1 -2i)=

-9 + 18i + 18i -16i^2 / 1^2 -4i^2 =

-9 + 26i + 16 / 1 + 4 =

7 + 26i / 5

Answer 7

idk what all of that means

Answer 8

anyone want to check my work?

Answer 9

\[\frac{-9+8i}{1+2i} \cdot \frac{1-2i}{1-2i}=\frac{-9+18i+8i-16i^2}{1-4i^2}=\frac{16-9+26i}{5}\]
\[=\frac{7+26i}{5}\]

Answer 10

gj