Difference between revisions of "HWK2MA425Fall2009" - Rhea

Revision as of 07:59, 3 September 2009

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 [http://www.math.purdue.edu/~bell/MA425/hwk2.txt HWK 2 problems]
-Here's a hint on I.8.3 --[[User:Bell|Bell]]
-It is straightforward to show that
-<math>(z,w)\mapsto z+w</math>
-is a continuous mapping
-<math>(\mathbb C\times \mathbb C)\to\mathbb C</math>
-because
-<math>|(z+w)-(z_0+w_0)|\le|z-z_0|+|w-w_0|</math>
-and to make this last quantity less than epsilon, it suffices to take
-<math>|z-z_0|<\epsilon/2</math>
-and
-<math>|w-w_0|<\epsilon/2.</math>
-To handle complex multiplication, you will need to use the standard trick:
-<math>zw-z_0w_0 = zw-zw_0+zw_0-z_0w_0=z(w-w_0)+w_0(z-z_0)</math>.