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GIVEN: $z_1=\\var{z1}$, $z_2=\\var{z2}$, $z_3=\\var{z3}$

FIND: Perform the following operations with the complex numbers and enter your answers to 3 decimal places.

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$z_1^*=$[[0]]

$z_1+z_2=$[[0]]

$z_1-z_3=$[[0]]

$z_2 \\cdot z_3=$[[0]]

$z_1 \\div z_3=$[[0]]

$\\frac{(\\var{z1})(\\var{z2})}{(\\var{z3})}=$[[0]]

$\\frac{(\\var{z3})}{(\\var{z1})(\\var{z2})}=$[[0]]

$|{\\var{z2}}|=$[[0]] and arg$({\\var{z2}})$=[[1]]

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FInd the distance between $(\\var{z1})$ and $(\\var{z3})$: [[0]]

$z_3 \\cdot z_3^*=$[[0]]

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prodz3z3star

", "templateType": "anything", "name": "prodz3z3star"}, "subz1z3": {"definition": "z1-z3", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "subz1z3"}, "addz1z2": {"definition": "z1+z2", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "addz1z2"}, "argz2": {"definition": "precround(arg(z2),3)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "argz2"}, "comboz123": {"definition": "precround((z1*z2)/z3,3)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "comboz123"}, "z1": {"definition": "random(-10..10)+random(-10..10 except 0)*i", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "z1"}, "quotz1z3": {"definition": "precround(z1/z3,3)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "quotz1z3"}, "prodz2z3": {"definition": "z2*z3", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "prodz2z3"}, "z1Conj": {"definition": "conj(z1)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "z1Conj"}, "modz2": {"definition": "precround(abs(z2),3)", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "modz2"}, "z3": {"definition": "random(-10..10 except [0,re(z1),re(z2)])+random(-10..10 except [0,im(z1),im(z2)])i", "group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "z3"}}, "name": "PreCal Operations with Complex Numbers", "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}]}]}], "contributors": [{"name": "Terry Young", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3130/"}]}