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Complex Number : Exercise 2

math2ever
Introduction
Exercise 2 will focus more on
  • Argand's diagram - Modulus and Argument
  • Complex numbers in polar, trigonometry and exponential forms
  • Multiplication and division of complex number in polar and trigonometry forms.
  1. Find the modulus and the argument each of the complex numbers below.





  2. Find the modulus and the argument each of the complex numbers.




  3. Plot each of the following complex numbers on separate Argand's Diagrams and find its modulus and argument.








  4. If z 1 =5+3i MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbiqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOEamaaBaaaleaacaaIXaaabeaakiabg2da9iaaiwdacqGHRaWkcaaIZaGaamyAaaaa@3B80@ and z 2 =6i+4 MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbiqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOEamaaBaaaleaacaaIYaaabeaakiabg2da9iabgkHiTiaaiAdacaWGPbGaey4kaSIaaGinaaaa@3C70@ , find the modulus and argument on each of the following cases.








  5. Express each of the following in the polar form, trigonometry form and exponential form.





  6. Express each of the following the trigonometry form.






  7. Express each of the following in polar and exponential form.





  8. Express the complex number z in Cartesian form its form when (arg z in radian).










  9. If z 1 =5 π 6 MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbiqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOEamaaBaaaleaacaaIXaaabeaakiabg2da9iaaiwdacqGHGic0daWcaaqaaiabec8aWbqaaiaaiAdaaaaaaa@3D1E@ and z 2 =4 π 4 MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbiqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOEamaaBaaaleaacaaIYaaabeaakiabg2da9iaaisdacqGHGic0cqGHsisldaWcaaqaaiabec8aWbqaaiaaisdaaaaaaa@3E09@ , find





  10. If z 1 = 5 ( cos30°+isin30° ) MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbiqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOEamaaBaaaleaacaaIXaaabeaakiabg2da9maakaaabaGaaGynaaWcbeaakmaabmaabaGaci4yaiaac+gacaGGZbGaaG4maiaaicdacqGHWcaScqGHRaWkcaWGPbGaci4CaiaacMgacaGGUbGaaG4maiaaicdacqGHWcaSaiaawIcacaGLPaaaaaa@48E2@ and z 2 =2( cos45°+isin45° ) MathType@MTEF@5@5@+=feaagaart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbiqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOEamaaBaaaleaacaaIYaaabeaakiabg2da9iaaikdadaqadaqaaiGacogacaGGVbGaai4CaiaaisdacaaI1aGaeyiSaaRaey4kaSIaamyAaiGacohacaGGPbGaaiOBaiaaisdacaaI1aGaeyiSaalacaGLOaGaayzkaaaaaa@48C7@ , find

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