- anonymous

Simplify the following quotient of complex numbers into the form a + bi. -9+8i/1+2i

- katieb

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- anonymous

You going to mutiply the numorator and the denominatior by the conjugate. Does that help?

- anonymous

so multiply -9 and 1 right

- anonymous

multiply top and bottom of the quotient by the conjugate of 1 + 2i which is 1 - 2i

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## More answers

- anonymous

huh I am confused

- anonymous

Your goal here is to "kill" the bottom complex number. you can do this by
\[(9+8i/1+2i) * (1 - 2i / 1 - 2i)\]
remember that 1-2i / 1-2i = 1 and you can multiply anything by 1

- anonymous

without changing the number

- anonymous

okay

- anonymous

(-9 + 8i)(1-2i)
------------
(1+2i)(1-2i)
the denominator simplifies to 1 + 4 = 5

- anonymous

so I take and combine like terms right?

- anonymous

yep. you'll find that if you multiply a complex number by its conjugate then you kill all of the i terms and just be left with real numbers

- anonymous

after I get the )-9+8i)(1-2i)

- anonymous

so it will be -9*1 and 8i*-2i?

- anonymous

yes - u now simplify the top expression
then divide by 5

- anonymous

no
remember
(a+b)(a+b) = a^2 + 2ab + b^2

- anonymous

so -9 - 16i/5 is what it should look like right

- anonymous

nope. your top term is off. Try using FOIL on the top again and see if you get somthing else.

- anonymous

okay lemme see (-9+8i)(1-2i) combine like terms -9*1=-9 8i*2i=16i total is -9+16i/5 is that right

- anonymous

(-9 + 8i)(1-2i) = -9 + 18i + 8i + 16 = 7 + 26i
the second bracket is first multiplied by -9 then its multuplied by + 81

- anonymous

by +8i

- anonymous

oh okay wasn't seeing how it was done that is why I was confuzzled

- anonymous

I dont know if this will help but treat i just like you would x when your distributing! I find that thinking about it that way very helpfful

- anonymous

final result is
7/5 + (26/5) i

- anonymous

okay so in algebra they try to change things up so it confuses you?

- anonymous

Thank you Jimmy you was very helpful as was you Walleye

- anonymous

yw!

- anonymous

thats ok

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