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Question

if z1= 7-3i, z2= 3 + root3 i , z3=4-8i, then find z1z2z3.

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Solution

z1=7-3iz2=3+3iz3=4-8iSo, z1z2z3=(7-3i)(3+3i)(4-8i)=(21+73i-9i-33i2)(4-8i)=(21+73i-9i-33(-1))(4-8i) As i2=-1=(21+73i-9i+33)(4-8i)=84-168i+283i-563i2-36i+72i2+123-243i=84-168i+283i-563(-1)-36i+72(-1)+123-243i=84-168i+283i+563-36i-72+123-243i=12-204i+43i+683=12+683-i(51-3)

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