SOLUTION: If a+b=2, then 2-a=b & 2-b=a And (1-i)a+(1+i)b=0, define a&b My attempt: (1-i)a+(1+i)b=0 (a-ai)+(b+bi)=0 (a+b)+(-ai+bi)=o (2)+(-(2-b)i+bi)=0 2+(-2i+bi+bi)=0 2+(-2i+bi^2)=

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: If a+b=2, then 2-a=b & 2-b=a And (1-i)a+(1+i)b=0, define a&b My attempt: (1-i)a+(1+i)b=0 (a-ai)+(b+bi)=0 (a+b)+(-ai+bi)=o (2)+(-(2-b)i+bi)=0 2+(-2i+bi+bi)=0 2+(-2i+bi^2)=      Log On


   

Question 887639: If a+b=2, then 2-a=b & 2-b=a
And (1-i)a+(1+i)b=0, define a&b
My attempt:
(1-i)a+(1+i)b=0
(a-ai)+(b+bi)=0
(a+b)+(-ai+bi)=o
(2)+(-(2-b)i+bi)=0
2+(-2i+bi+bi)=0
2+(-2i+bi^2)=0
2+(-2i-b)=o
2-b+(-2i)=o
2-2i=b,?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
a%2Bb=2
%281-i%29a%2B%281%2Bi%29b=0
.
.
.
From eq. 2,
a-ai%2Bb%2Bbi=0
%28a%2Bb%29%2B%28-ai%2Bbi%29=0
%28a%2Bb%29%2Bi%28b-a%29=0
2%2Bi%28b-a%29=0
i%28b-a%29=-2
b-a=-2%2Fi
b-a=%28-2i%29%2Fi%5E2
3.b-a=2i
Adding together eqs.1 and 3,
a%2Bb%2Bb-a=2%2B2i
2b=2%2B2i
highlight%28b=1%2Bi%29
Then using eq. 1,
a%2B%281%2Bi%29=2
highlight%28a=1-i%29