Can two different numbers have the same absolute value?

Question

Mila Anderson · Accepted Answer

Yes.

The magnitude of a number, regardless of its sign, is its absolute value. Hence there can be two real numbers with different signs such #+a# and #-a# who have an absolute value of #a#. Other examples could be #+1.01001000100001.....# and #-1.01001000100001.....# who have different signs but same absolute value, or for that matter #-root(3)73# and #+root(3)73#. Therefore, if the domain is a real number, then two distinct numbers can have the same absolute value for every value. However, if domain is Complex numbers, absolute value of a number #a+bi# is #sqrt(a^2+b^2)# and for each absolute value there could be infinite different numbers with same absolute value. For example, #3+4i#, #-4+3i#, #1+i2sqrt6#, #-5-i2sqrt5#, #-5i# all have an absolute value of #5#.

Jeremiah Andrews · Answer

undefined Yes, two different numbers can have the same absolute value. Absolute value refers to the distance of a number from zero on the number line, regardless of its sign. For example, both 5 and -5 have an absolute value of 5. Similarly, 3 and -3 have the same absolute value, which is 3. In general, any positive number and its corresponding negative counterpart will have the same absolute value.