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Complex Number : Exercise 1

math2ever
Introduction
In Exercise 1, basic concepts of complex number are highlighted including

  • Simplification of i n MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbiqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyAamaaCaaaleqabaGaamOBaaaaaaa@374C@
  • complex conjugate
  • Algebra operations in complex number - Addition, Subtraction, Multiplication, Division and Equality
  1. Express each of the following complex numbers in the form of a + bi.







  2. Simplify each of the followings.








  3. Simplify each of the following by addition or subtraction.







  4. Simplify each of the followings.











  5. Given that express in the form of a+ bi.






  6. Given that z=2+i MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbiqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOEaiabg2da9iabgkHiTiaaikdacqGHRaWkcaWGPbaaaa@3ABC@ , express z+ 1 z MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbiqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOEaiabgUcaRmaalaaabaGaaGymaaqaaiaadQhaaaaaaa@38E9@ in the form of a+ bi

  7. Given that z=23i MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbiqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOEaiabg2da9iaaikdacqGHsislcaaIZaGaamyAaaaa@3A97@ , express z 1 z 2 MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbiqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacaWG6baabaGaaGymaiabgkHiTiaadQhadaahaaWcbeqaaiaaikdaaaaaaaaa@39DD@ in the form of a+ bi
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