Complex things

this is the way i did it......

I ve taken z = iz as the line x+y=0 ths part i'm not sure whether i am right...

so the reflection of 2-i i.e (2,-1) in the line x+y=0 is coming out to be (1,-2) i.e 1-2i

please point out my mistake if am wrong somewhere...

now given equation of straight line is y = -x
hence reflection of 2,-1 abt y= - x is 1 , -2
hence required complex no. is 1 - 2i

hence required answer [1]

z(bar)=iz
is
y=x

reason

take
z = a+ia
z(bar)=a-ia
z=iz(bar) rotation by 90 degree

so it shud be

y=x

let reflection be

x,y

now we have

2+x=y-1
y=x+3

also we have

1+y=2-x

y=1-x

solve both

we get
x=-1 .y=2

so answer is

(-1,2i )

nope i was wrong
i took direction of rotation wrong

proof by graph

take

z=x-ix

now rotate it by 90 in anticlockwise direction

hence

iz= =z(bar)

but RSP bhaiya is it necessary to take z=x-ix...why cant we take z=x+ix....
[12]

i suppose it is done oral[3][3]........n answer i suppose shud come[1-2i]

if u didnt understand plese see coni's theorem [1]

@sandipan...........no doubt...u r a genius man[1]
@rpf........i knew it man....just saying was it really needed???[1]