SOLUTION: The set of non-zero complex numbers is closed under which operation(s)?

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Question 53194: The set of non-zero complex numbers is closed under which operation(s)?
Answer by venugopalramana(3286) About Me  (Show Source):
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The set of non-zero complex numbers is closed under which operation(s)?
ADDITION
(A+IB)+(P+IQ)=(A+P)+I(B+Q)...IF A=-P AND B=-Q,IT GIVES ZERO WHICH IS NOT IN THE SET.HENCE NOT CLOSED
SIMILARLY
MULTIPLICATION
(A+IB)(P+IQ)=(AP-BQ)+I(AQ+BP)...HERE IF AP=BQ THEN AQ CANNOT EQUAL -BP AND
VISEVERSA..HENCE IT IS NONZERO COMPLEX NUMBER..SO IT IS CLOSED
DIVISION
(A+IB)/(P+IQ)=(A+IB)(P-IQ)/(P^+Q^2)=[(AP+BQ)+I(BP-AQ)]/(P^2+Q^2)
FOR SAME REASON AS ABOVE ..WE GET THIS ALSO AS CLOSED