# Complex Numbers and Analytic Functions

Prove algebraically that for complex numbers,

|z1| - |z2| (is less than or equal to) |z1 + z2| (is less than or equal to) |z1| + |z2|

Interpret this result in terms of two-dimensional vectors. Prove that

|z-1| < |sqrt(z^2 - 1) < |z + 1|, for H(z) > 0.

Show that complex numbers have square roots and that the square roots are contained in the complex plan. What are the square roots of i?

(See attached for full problem)

© BrainMass Inc. brainmass.com October 10, 2019, 7:52 am ad1c9bdddfhttps://brainmass.com/math/complex-analysis/complex-numbers-analytic-functions-598464

#### Solution Preview

Hello and thank you for posting your question to Brainmass.

The solution ...

#### Solution Summary

The solution illustrates how to show that any complex number has a square root, and how to construct an analytic function.

$2.19