What is modulus z complex in z = (1+2i)/(1-i)?
1 Answer | Add Yours
Modulus or magnitude or absolute value of a complex number `z = x + i*y` is given by the following formula, such that:
`|z| = sqrt(x^2 + y^2)`
You also need to remember the properties of absolute value, such that:
`|(z_1)/(z_2)| = |z_1|/|z_2|`
Hence, identifying `z_1 = 1 + 2i` and `z_2 = 1 - i` , you may evaluate the followings:
`|z_1| = sqrt(1^2 + 2^2) => |z_1| = sqrt(1+4) => |z_1| = sqrt5`
`|z_2| = sqrt(1^2 + (-1)^2) => |z_2| = sqrt 2`
Hence, replacing `sqrt5` for `|1 + 2i|` and `sqrt 2` for `|1 - i|` yields:
`|1 + 2i|/|1 - i| = sqrt5/sqrt2 =>|1 + 2i|/|1 - i| = (sqrt5*sqrt2)/2`
`|1 + 2i|/|1 - i| = sqrt10/2`
Hence, evaluating the modulus of the given complex number `z = (1 + 2i)/(1 - i)` yields `|z| = |1 + 2i|/|1 - i| = sqrt10/2` .
Join to answer this question
Join a community of thousands of dedicated teachers and students.Join eNotes