How do you find #abs(-5i)#?

1 Answer
sente
Jun 6, 2016

Apply the definition #|a+bi| = sqrt(a^2+b^2)# to find that

#|-5i| = 5#

Explanation:

The modulus of a complex number #a+bi#, denoted #|a+bi|#, is given by

#|a+bi| = sqrt(a^2+b^2)#.

and is an extension of the absolute value function, which applies to reals. The latter represents the distance from the real number to #0# on the number line, and the former represents the distance of the complex number to the origin on the complex plane.

Applying this definition to our given complex number, we have:

#|-5i| = |0+(-5)i|#

#=sqrt(0^2+(-5)^2)#

#=sqrt(0+25)#

#=sqrt(25)#

#=5#

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