0
The absolute value of a number is defined conceptually as its distance from 0. The absolute value of a complex number is therefore defined by the distance formula:
|z| = sqrt(re(z)2 - im(z)2)
0 is a complex number, as is proven as follows:
A complex number is a number of the form x + yi, where x and y are numbers.
0i = 0.
0 = 0 + 0.
0 = 0 + 0i.
0 = x + yi where x and y are 0.
0 is a number.
Therefore, 0 is a complex number.
As such, the distance formula can be used to calculate |0|:
|0| = sqrt(re(0)2 - im(0)2)
= sqrt(02 - 02)
= sqrt(0 - 0)
= sqrt(0)
= 0
Still curious? Ask our experts.
Chat with our AI personalities
Professor
Devin
RossAdd your answer:
Earn +20 pts
What is the absolute value of -4?
0
What is the absolute value of -4.2?
The absolute value of a number is the distance from that number to 0. Therefore, the absolute value is ALWAYS positive. the absolute value of -4.2 is 4.2 To find the absolute value, just determine how far it is from 0.
What is the integer's absolute value?
An interger's absolute value is how far away it is from 0, so an interger's absolute value will always be positive. The absolute value of -83 is 83. The absolute value of 178 is 178. etc.
How do you find the absolute value of something?
If a number is not less than zero then that is its absolute value. If a number is less than zero, its negative is its absolute value. So, if |x| denotes the absolute value of x, then |x| = -x for x<0 [since if x<0 then -x>0] and |x| = x for x>= 0
Is this question true or false are there always two numbers thtj have the same absolute value?
Other than for the value 0, there are always two numbers that have the same absolute value: the number and the negative of the number, eg 2 and -2 both have the absolute value 2. There is no negative 0, so there is only the number 0 which has the absolute value 0.
