A community for students.
Here's the question you clicked on:
 0 viewing
Sinz
 4 years ago
Simplify the following quotient of complex numbers into the form a + bi. 9+8i/1+2i
Sinz
 4 years ago
Simplify the following quotient of complex numbers into the form a + bi. 9+8i/1+2i

This Question is Closed

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

Sinz
 4 years ago
Best ResponseYou've already chosen the best response.0so multiply 9 and 1 right

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

Walleye
 4 years ago
Best ResponseYou've already chosen the best response.0Your 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

Walleye
 4 years ago
Best ResponseYou've already chosen the best response.0without changing the number

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

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

Walleye
 4 years ago
Best ResponseYou've already chosen the best response.0yep. 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

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

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

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

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

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

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

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

jimmyrep
 4 years ago
Best 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

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

Walleye
 4 years ago
Best ResponseYou've already chosen the best response.0I 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

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

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

Sinz
 4 years ago
Best ResponseYou've already chosen the best response.0Thank you Jimmy you was very helpful as was you Walleye
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.