Question

1. Show that |z − w| ≤ |z − t| + |t − w| for all z, w, t ∈ C.

2.Does every complex number have a multiplicative inverse? Explain

3.Give a geometric interpretation of the expression |z − w|, z, w ∈ C.

4.Give a lower bound for |z + w|. Show your result.

5.Explain how to compute the inverse of a nonzero complex number z geometrically.

6.Explain how to compute the conjugate of a complex number z geometrically.

7.Explain how to subtract complex numbers geometrically.

Thank you

Answer #1

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