Satz 4.17 Für komplexe Zahlen z,z1,z2 gilt:

(1) | z 1 |0, und | z |=0z=0, (2) | z |=| z |, (| z 1 z 2 |=| z 2 z 1 |) (3) | z 1 z 2 |=| z 1 || z 2 |, (| z n |= | z | n ) (4) | z 1 z 2 |= | z 1 | | z 2 | , fall z 2 0, (5) | z 1 + z 2 || z 1 |+| z 2 |, (6) | | z 1 || z 2 | || z 1 z 2 |. MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaqGOa GaaeymaiaabMcacaqGGaWaaqWaaeaacaWG6bWaaSbaaSqaaabaaaaa aaaapeGaaGymaaWdaeqaaaGccaGLhWUaayjcSdGaeyyzImRaaGimaG qaciaa=XcacaWFGaGaa8xDaiaa=5gacaWFKbGaa8hiamaaemaabaGa amOEaaGaay5bSlaawIa7aiabg2da9iaaicdacqGHuhY2caWG6bGaey ypa0JaaGimaiaacYcaaeaacaqGOaGaaeOmaiaabMcacaqGGaWaaqWa aeaacqGHsislcaWG6baacaGLhWUaayjcSdGaeyypa0ZaaqWaaeaaca WG6baacaGLhWUaayjcSdGaaeilaiaabccacaqGOaGaeyO0H49aaqWa aeaacaWG6bWaaSbaaSqaa8qacaaIXaaapaqabaGccqGHsislcaWG6b WaaSbaaSqaa8qacaaIYaaapaqabaaakiaawEa7caGLiWoacqGH9aqp daabdaqaaiaadQhadaWgaaWcbaWdbiaaikdaa8aabeaakiabgkHiTi aadQhadaWgaaWcbaWdbiaaigdaa8aabeaaaOGaay5bSlaawIa7aiaa bMcaaeaacaqGOaGaae4maiaabMcacaqGGaWaaqWaaeaacaWG6bWaaS baaSqaa8qacaaIXaaapaqabaGcpeGaeyyXICTaamOEa8aadaWgaaWc baWdbiaaikdaa8aabeaaaOGaay5bSlaawIa7aiabg2da9maaemaaba GaamOEamaaBaaaleaapeGaaGymaaWdaeqaaaGccaGLhWUaayjcSdWd biabgwSixpaaemaabaGaamOEa8aadaWgaaWcbaWdbiaaikdaa8aabe aaaOWdbiaawEa7caGLiWoacaqGSaGaaeiiaiaabIcacqGHshI3daab daqaaiaadQhapaWaaWbaaSqabeaapeGaamOBaaaaaOGaay5bSlaawI a7aiabg2da9maaemaabaGaamOEaaGaay5bSlaawIa7a8aadaahaaWc beqaa8qacaWGUbaaaOWdaiaabMcaaeaacaqGOaGaaeinaiaabMcaca qGGaWaaqWaaeaadaWcaaqaaiaadQhadaWgaaWcbaWdbiaaigdaa8aa beaaaOqaaiaadQhadaWgaaWcbaWdbiaaikdaa8aabeaaaaaakiaawE a7caGLiWoacqGH9aqpdaWcaaqaamaaemaabaGaamOEamaaBaaaleaa peGaaGymaaWdaeqaaaGccaGLhWUaayjcSdaabaWaaqWaaeaacaWG6b WaaSbaaSqaa8qacaaIYaaapaqabaaakiaawEa7caGLiWoaaaGaa8hl aiaa=bcacaWFMbGaa8xyaiaa=XgacaWFSbGaa83Caiaa=bcacaWG6b WaaSbaaSqaa8qacaaIYaaapaqabaGccqGHGjsUcaaIWaGaaeilaaqa aiaabIcacaqG1aGaaeykaiaabccadaabdaqaaiaadQhadaWgaaWcba Wdbiaaigdaa8aabeaakiabgUcaRiaadQhadaWgaaWcbaWdbiaaikda a8aabeaaaOGaay5bSlaawIa7aiabgsMiJoaaemaabaGaamOEamaaBa aaleaapeGaaGymaaWdaeqaaaGccaGLhWUaayjcSdGaey4kaSYaaqWa aeaacaWG6bWaaSbaaSqaa8qacaaIYaaapaqabaaakiaawEa7caGLiW oacaGGSaaabaGaaeikaiaabAdacaqGPaGaaeiiamaaemaabaWaaqWa aeaacaWG6bWaaSbaaSqaa8qacaaIXaaapaqabaaakiaawEa7caGLiW oacqGHsisldaabdaqaaiaadQhadaWgaaWcbaWdbiaaikdaa8aabeaa aOGaay5bSlaawIa7aaGaay5bSlaawIa7aiabgsMiJoaaemaabaGaam OEamaaBaaaleaapeGaaGymaaWdaeqaaOGaeyOeI0IaamOEamaaBaaa leaapeGaaGOmaaWdaeqaaaGccaGLhWUaayjcSdGaaeOlaaaaaa@F4D1@