SOLUTION: Prove that |z1+z2| < or = |z1| + |z2|. Use |z|^2 = conjugate (z) times z, Re(z) = (z + conjugate (z)) / 2, and Re(z) < or = |z|. This inequality is known as the Triangle Inequality

Question 1181369: Prove that |z1+z2| < or = |z1| + |z2|. Use |z|^2 = conjugate (z) times z, Re(z) = (z + conjugate (z)) / 2, and Re(z) < or = |z|. This inequality is known as the Triangle Inequality.
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Let denote the conjugate of the complex number .

Then

=

= , from the fact Re(z) = (z + conjugate (z)) / 2.

, from the fact Re(z) < or = |z|.

===>
Since both and are non-negative, the last inequality implies that

, and the Triangle Inequality is proved.
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