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Three complex numbers z1,z2,z3 are given by

z1=5-7j, z2 =5+8j, z3 =-8-2j

(i) Find 4z1 + 7z2 - 6z3

(ii) Find Z1 Z2

(iii) Find Z2/Z3

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2 ANSWERS


  1. i)4(5-j7)+7(5+j8)- 6(-8-j2)

    20-j28+35+j56+42+j16

    combine like terms

    95+j46

    ii) not enough info

    iii)(5+j8)/(-8-j2)

    multiply top and bottom by complex conjugate of Z3

    (5+j8)*(-8+j2)/(-8-j2)*(-8+j2)  

    Z3*Z3conjugate becomes (-8)^2+j^2=68

    (5+j8)*(-8+j2)/68

    then just multiply it using FOIL(first outside inside last) and remember j^2=(-1)


  2. [5-7J]*[5+8J]=   25+40J-35J-56J2=    J[40-35-56J]+25=    30-56J

    5+8J/8-2J=     5+4J=8     4J=3

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