Aquí tienen las soluciones a los ejercicios 4 y 6 de la tarea 1.
![4a](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_saNv1dHLvRYU-CmBWMo2qXxEFFz3eifLHOOzuz3GwiwIKzW96JD90hnq-9Xvr20WlYs6bSksFTZ4-wniLlHU7oIOKAhy8mNu19LNwxx8B-zWnmQnr9lW2Uy9Xzfq7p8a3ZlBtZybQNLigQ=s0-d)
![4e](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_tXHKrn0F6RNDfGuuASV_uqEwyJBWldadhYTSmCQEyD7sAxqeqhDG0794JiQvvhysXl4xsYYBa2PVX5QBXNZkqYLcRV2Rl-fQuivrVztylycoLNIvqXCeO9rFEe9Grh9PahP8hBFolRMLXc=s0-d)
![4c](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_uYm2OPnB_CNoLFO0wmMt_km6cPPoCmGbas12R6OdKRxdLBGBQJyWt1d86tneZuh2EsLNxhpIiTm08ACZW1ydaMgCDU5T4p8DghwJFqjpVdyx45pIWASWbx63Ct5pH2ZRL5JbN8Mico9Kk=s0-d)
![4d](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_vbJJ1FEERGg5cdBexlA5nd3tGf0atqgdhOy4LUU1Hso1kM13keKczw_xBX6dChJ4s5lAaE8Tq9K2YL1wx3Vx-kmd9csYN5iitP0UuWabB49yrM8N-zuBajZ5g3qlpwSc54tkK4P626=s0-d)
![6a](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_uRxsY9jLOvWiqBCOPy-wTIr8islB5LUn0B_iUxYjSXu5n5Z2Usx5XygjTYk60D3JYy1byrTDKoNnsGE4y48PZoiZPxpuAcw9obTS_gagr81NDUOE5Yu0BFOtGRR8ym4OVpi9W1UMFvslM=s0-d)
![6b](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_srTQ9SBPJoRpmvadn04HdqM8YOc1JsxQ9JtMszRl_zUW7CAYSn9ApUb5wMKDs5zPItd3bt9G-VqWHUCabHo8Iq1mKQLr0XdvddafHhxxTDG06YHFyuSwZUfjj9dSpJpMxEfOiFxPqXcdM=s0-d)
![6c](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_tndAiBsf9-VAO-30fV2AL6UesBLiHznratMhspwkNtWNHMbyiIgOxi4amLd2toP76M0cg4o7eqQwTCPZp4gfjuHtLtrbu-85tgKaM6w85cl_k647apUM95jgY5u2l1TwMfFOSZY5QKXCI=s0-d)
![6d](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_uncQOBnDi6jMfOzc5vkuhoBnIrYESieBJ7yQoTpeYrh0iDBPC0LR7Svnf04HI4Db_NsrC-ZtEoiYcIzOkNhulV8Lc3DbGUIuuMDXhHriY6YnpVu5QhXz2E--DiFFbb_sXuJ3SKERtjNhw=s0-d)
$Latex A=-1$
![6e6](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_seA6yKMdUhYbalfEyC8uuyL6Iu1G4UCWPF7c4z0guH_8Myrd-ifzUvjUbcMc8go1BFTIv-Ohb_8nZaTnYxhiECpH4l4ETTxc_300aJ0vkCyK12ljGrTokQBFopfyWhmM8oxIiyMzOqYNyf=s0-d)
$Latex A=-\frac{3}{4}$
![6e5](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_uhE24WoTi6A5FSgUni6FgBP0P2nCVLcSJXdB-NBCHonWwMQHgecLkRcFMN6_eloaJrWOjPlVxVWreJ9Fv0JPXv_ibxv1KVs4TRjnQFAGJfmlCiLnjrDCLdM3OeZLBzZgA7VBEFOEdfsFI=s0-d)
$Latex A=-\frac{1}{2}$
![6e1](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_uW08-k-Lg9tc3z1aAH0wrX4o033vXSZsXNmpMAOB_rqOEfsiB4hW423gmd4Pk-E2j1sr8w2yuDprHzH6d9jaMbcffGUXb9c5Pi5gukdQRipVDIdLwzKbvXAox4G84SnMJPIjlw5Ktkn1hO=s0-d)
$Latex A=-\frac{1}{8}$
![6e7](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_vo4PtVXmntqyolA0wOW8x8CuxaLcE8vLJ-1huZ522MZr8qCE3YdNr7Qn6KLi9CIBTLo1O0MmzE25z03bqnUBdmD8d87aupGK-VgyeoUazklP3GJbPWF6c0TPzFaILApPQQ9vY20rW7de3S=s0-d)
$Latex A=0$
![6e2](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_vWYxTCplD098YCfvxAyruw52-W7CJiu9XSSTu4A7hmhSJHdHLqxWjWlzSEw-O0aq0HY7LVy3dkKZIki7XRPuV6pBeMZKo6XfCvw-DbkL0pSrQ64h4-jT7fsI6XEDRmmntO43vRdHVV5T0u=s0-d)
$Latex A=\frac{1}{4}$
![6e3](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_sz_NJZmAoUBWpES80aYi6RXIoNsJgmoJFFZoTwrztFSCb4R49kB05K3V6U8XQUWt1Qw6LuydZ4NUPZ2X-3kL2qe62q41R201UctiVwRHm7axrPN-WSRbpICvAILfCu8sQDQpAy9W1awE9A=s0-d)
$Latex A=\frac{2}{3}$
![6e4](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_sx3UkYKec8aqsn8_J-9E3jBaN5oSCC__T4HeSsZrVYUypoGirqHw3lCvWw8qX3xITAfZ1vRicdqYB_aBIw7VJ299l0oOwUaBIDu93ZHc8QF6CebxhmPSxZmlifNPtUj0GsjYEcp4vskPDH=s0-d)
$Latex A=1$
![6e8](https://lh3.googleusercontent.com/blogger_img_proxy/AEn0k_vtbIZtQlHUvYmzFnhL7JwmQjkOtOKu8XRt1LMIFONuugha9z93iQFgYTInPHMG4OuygjjjGH0V6xIMQS6jGUXVzrv6tk2Vr2SVYzoUuMrdJRQFx4BjjQvOR8GRLmJgqUBtgyLUEXdPIMDz=s0-d)
Ejercicio 4
- $Latex |\arg z|\le \frac{\pi}{4}$.
- $Latex 0<\arg{z-1-i}<\frac{\pi}{3}$.
- $Latex |z|<\arg z$.
- $Latex \log|z|=\arg z$.
Ejercicio 6
- Hemisferio interior $Latex Z\le0$.
- Tapa polar $Latex 3/4\le Z\le1$.
- Líneas de latitud $Latex X=\sqrt{1-Z^2}\cos{\theta}, Y=\sqrt{1-Z^2}\sin{\theta}$ para $Latex Z$ fijo (en este caso $Latex Z =\frac{1}{2}$) y $Latex 0\le\theta\le2\pi$.
- Líneas de longitud $Latex X=\sqrt{1-Z^2}\cos{\theta}, Y=\sqrt{1-Z^2}\sin{\theta}$ para $Latex \theta$ fijo (en este caso $Latex \theta =\frac{\pi}{4}$) y $Latex -1\le \theta \le 2\pi$.
- Tapa esférica $Latex A\le X\le1$ con centro sobre el ecuador para $Latex A$ fijo.
$Latex A=-1$
$Latex A=-\frac{3}{4}$
$Latex A=-\frac{1}{2}$
$Latex A=-\frac{1}{8}$
$Latex A=0$
$Latex A=\frac{1}{4}$
$Latex A=\frac{2}{3}$
$Latex A=1$
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