Q. Define conjugate complex numbers and show that their sum and product are real numbers.

Asked by imabhi264 | 21st Jun, 2017, 10:08: PM

Expert Answer:

begin mathsize 16px style The space conjugate space complex space numbers space are space the space numbers space whose space real space and space imaginary space parts space are space equal
but space of space opposite space signs.

For space example comma
Consider comma space straight a plus bi space and space straight a minus bi space are space conjugate space complex space numbers space but space sign space of space straight b space are space opposite.
straight a plus bi plus straight a minus bi equals 2 straight a space which space is space purely space real space number.
Also comma
open parentheses straight a plus bi close parentheses cross times open parentheses straight a minus bi close parentheses equals straight a squared minus open parentheses bi close parentheses squared
open parentheses straight a plus bi close parentheses cross times open parentheses straight a minus bi close parentheses equals straight a squared minus open parentheses straight b squared straight i squared close parentheses
open parentheses straight a plus bi close parentheses cross times open parentheses straight a minus bi close parentheses equals straight a squared minus straight b squared cross times open parentheses negative 1 close parentheses space space space space space space open parentheses straight i squared equals negative 1 close parentheses
open parentheses straight a plus bi close parentheses cross times open parentheses straight a minus bi close parentheses equals straight a squared plus straight b squared
Which space is space also space purely space real space number. end style

Answered by Sneha shidid | 22nd Jun, 2017, 09:30: AM