If-the-points-1-2i-and-1-4i-are-reflections-of-each-other-in-the-line-z-1-i-z-1-i-K-0-then-the-value-of-K-is-

Question Number 140444 by EnterUsername last updated on 07/May/21

If the points 1 + 2 i and - 1 + 4 i are reflections of

each other in the line z (1 + i) + \bar{z} (1 - i) + K = 0, then

the value of K is_____.

Answered by mr W last updated on 08/May/21

m i d p o i n t f r o m 1 + 2 i a n d - 1 + 4 i i s 3 i,

w h i c h l i e s o n t h e l i n e .

z = 3 i, \bar{z} = - 3 i

3 i (1 + i) - 3 i (1 - i) + k = 0

3 i - 3 - 3 i - 3 + k = 0

\Rightarrow k = 6

Commented by EnterUsername last updated on 12/May/21

Thanks