Question

The following statements concern the modulus. Which statement is false?

Answer 1

we will check each options

option-A:

The modulus represents the distance between the complex number and the origin

we know that modulus is a kind of distance

For example: if we have to find modulus of x+iy

we get

$|z|=\sqrt{x^2+y^2}$

that is also distance between (0,0) and (x,y)

so, this is TRUE

option-B:

$|z|=\sqrt{x^2+y^2}$

It is also similar to Pythagoras theorem

so, this is also TRUE

option-C:

we got modulus formula

$|z|=\sqrt{x^2+y^2}$

we know that value of sqrt can never be negative because it will always result in positive value

so, this is FALSE

option-D:

$|z|=\sqrt{x^2+y^2}$

It is also similar to absolute value

so, this is TRUE