Solving Complex Numbers: How to Find the Angle for Non-Real Numbers

[zorro]

Homework Statement

sin^-1{z-1/i} where z is non real, can be angle of a triangle if

1)Re(z) = 1, Im(z) = 2
2)Re(z) = –1, 0<Im(z)≤1
3)Re(z) + Im(z) = 0
4)none of these

The Attempt at a Solution

-1≤z-1/i≤1, but inequalities don't hold for complex numbers. How to solve this one?

 

[HallsofIvy]

First, write it carefully. You mean (z- 1)/i. What you wrote would be z- (1/i).

Yes, inequalities don't hold for complex numbers. That means (z- 1)/i must be real. Writing z= x+ iy, we must have (x+ iy- 1)/i= a where a is real.