Determine whether the statements are true or false? Justify your answer
(a)the modulus of the sum of two complex numbers is equal to the difference of their moduli
(b)The modulus of the difference of two complex numbers is equal to the difference of their moduli
(a)the modulus of the sum of two complex numbers is equal to the difference of their moduli
(b)The modulus of the difference of two complex numbers is equal to the difference of their moduli
1 Answer
Mar 22, 2018
Both statements are false in general
Explanation:
The modulus of a complex number (or of a real number for that matter) is its non-negative distance from
A complex number (or real number) has modulus and direction.
By choosing direction appropriately, we can find counterexamples:
A counterexample to (a) would be:
#abs(1+1) = abs(2) = 2 != 0 = abs(1)-abs(1)#
A counterexample to (b) would be:
#abs(1-(-1)) = abs(2) = 2 != 0 = abs(1)-abs(1)#
