#16)What are the loci of points z which satisfy the followingrelations...? d.) 0

Question

#16)What are the loci of points z which satisfy the followingrelations...?

d.) 0 < Re(iz) < 1 ???

g.) < arg(z) < , < Re(z) < ,where -/2 < , < /2, > 0 ???

I'm also wondering for help with this proof:
#15)...Given:
z_1 + z_2 + z_3 = 0 and |z_1| + |z_2| + |z_3| = 1,
prove this defines an equilateral triangle inscribed in the unitcircle |z| = 1. Any hints? What should I show to provethis?

Thanks!

(PS - the book is available on Google Books for those interested inseeing the original problems. They're on page 9, numbers15/16.)

Explanation / Answer

Re (iz) = Re (i (x + iy)) = Re(ix -y)) = -y = - Im(z) so 0 Im(z) > -1 This is a horizontal strip in the complex plane. a

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