Complex Numbers

[Aladdin]

The questions says :

A , M and N are three distinct points of respective affixes i , z1 and z3.

If z2 = iz1 + 1 + i ,

then, triangle AMN is :

a)equilateral .
b)semi-equilateral
or
c)right isosceles.

I think the key word is DISTINCT . I know that two points to be distinct z must be different from z(bar) or its conjugate.

Any help will be greatly appreciated.
Thank You

 

[Aladdin]

Another Complex Numbers problem :

If z = -2( sin(pi/3) + icos(pi/3)

then argumant of the conjugate of z is ?

It's easy but the answer I'm getting is different from the given answers ,,,

Ok - z = -2(cos(pi/2 - pi/3) ) + isin(pi/2 - pi/3 )

z = -2(cos(pi/6) + isin(pi/6)

z = -2e^i(pi/6)

z = 2e^i(pi/6 + pi)

z = 2e^i(7pi/6)

But Arg(z) = -arg of conjugate ------> arg(zbar) = -7pi/6 ( This is my answer , but the given numbers which one of them is correct are :
-pi/6 , 5pi/6 , 7pi/6