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Engineering Mathematics Solutions

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Added on  2020-05-16

Engineering Mathematics Solutions

   Added on 2020-05-16

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Engineering Mathematics 1ENGINEERING MATHEMATICSby [NAME]CourseProfessor’s NameInstitutionLocation of InstitutionDate
Engineering Mathematics Solutions_1
Engineering Mathematics 2Engineering mathematicsPart 1Task 1The following expression represents two complex numbers which are to be multiplied.(A+jB)(C−jD)Carry out the operation working in rectangular formSince A=6, B=8, C=2 and D=4 the complex numbers become (6+j8)(2−j4)Therefore, the operation becomes, ¿12−j24+j16−32(j2)¿44−j8Polar forme1=√62+82 =10θ1=tan−186=53.43z1=10e53.43ie2=√22+42 =√20θ2=tan−142=63.43z2=√20e63.43i
Engineering Mathematics Solutions_2
Engineering Mathematics 344e116.56iThe above solution is equal to ¿44−j8therefore the two answers are similar. The solution can be presented on an Argand diagram as shown below.Task 2The following expression represents two complex numbers which ae to be divided.A+jBC−jDRectangular formSince A=6, B=8, C=2 and D=4 the complex numbers become 6+j82−j4The first step is multiplying the complex number with the conjugate of the denominator as follows;6+j82−j4×2+j42+j4=12+j24+j16−324+16
Engineering Mathematics Solutions_3
Engineering Mathematics 4=−20+j4020=−1+j2Polar forme1=√62+82 =10θ1=tan−186=53.43z1=10e53.43ie2=√22+42 =√20θ2=tan−142=63.43z2=√20e63.43iz=z1z2=10√20e−10.33The above solution is similar to ¿−1+j2therefore both methods give a similar result.The solution s represented as shown below
Engineering Mathematics Solutions_4

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