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

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WalleyeBest ResponseYou've already chosen the best response.0
You going to mutiply the numorator and the denominatior by the conjugate. Does that help?
 2 years ago

SinzBest ResponseYou've already chosen the best response.0
so multiply 9 and 1 right
 2 years ago

jimmyrepBest ResponseYou've already chosen the best response.2
multiply top and bottom of the quotient by the conjugate of 1 + 2i which is 1  2i
 2 years ago

WalleyeBest ResponseYou've already chosen the best response.0
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 12i / 12i = 1 and you can multiply anything by 1
 2 years ago

WalleyeBest ResponseYou've already chosen the best response.0
without changing the number
 2 years ago

jimmyrepBest ResponseYou've already chosen the best response.2
(9 + 8i)(12i)  (1+2i)(12i) the denominator simplifies to 1 + 4 = 5
 2 years ago

SinzBest ResponseYou've already chosen the best response.0
so I take and combine like terms right?
 2 years ago

WalleyeBest ResponseYou've already chosen the best response.0
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
 2 years ago

SinzBest ResponseYou've already chosen the best response.0
after I get the )9+8i)(12i)
 2 years ago

SinzBest ResponseYou've already chosen the best response.0
so it will be 9*1 and 8i*2i?
 2 years ago

jimmyrepBest ResponseYou've already chosen the best response.2
yes  u now simplify the top expression then divide by 5
 2 years ago

jimmyrepBest ResponseYou've already chosen the best response.2
no remember (a+b)(a+b) = a^2 + 2ab + b^2
 2 years ago

SinzBest ResponseYou've already chosen the best response.0
so 9  16i/5 is what it should look like right
 2 years ago

WalleyeBest ResponseYou've already chosen the best response.0
nope. your top term is off. Try using FOIL on the top again and see if you get somthing else.
 2 years ago

SinzBest ResponseYou've already chosen the best response.0
okay lemme see (9+8i)(12i) combine like terms 9*1=9 8i*2i=16i total is 9+16i/5 is that right
 2 years ago

jimmyrepBest ResponseYou've already chosen the best response.2
(9 + 8i)(12i) = 9 + 18i + 8i + 16 = 7 + 26i the second bracket is first multiplied by 9 then its multuplied by + 81
 2 years ago

SinzBest ResponseYou've already chosen the best response.0
oh okay wasn't seeing how it was done that is why I was confuzzled
 2 years ago

WalleyeBest ResponseYou've already chosen the best response.0
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
 2 years ago

jimmyrepBest ResponseYou've already chosen the best response.2
final result is 7/5 + (26/5) i
 2 years ago

SinzBest ResponseYou've already chosen the best response.0
okay so in algebra they try to change things up so it confuses you?
 2 years ago

SinzBest ResponseYou've already chosen the best response.0
Thank you Jimmy you was very helpful as was you Walleye
 2 years ago
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