# Which is the module of the complex number z = 3 - 4i ?Which is the module of the complex number z = 3 - 4i ?

### 5 Answers | Add Yours

You should remember that the absolute value of the complex number z is the magnitude of the vector whose coordinates are such that:

**Hence, evaluating the absolute value of the given complex number yields **

z= 3-4i

The module of z is lzl

We know that:

lzl = sqrt(a^2 + b^2)

= sqrt(9 + 16) = sqrt25

= 5

Then the module of z is:

**lzl = 5**

The module of a complex number z = a + bi is sqrt ( a^2 + b^2). We only consider the positive square root to calculate this.

Here we have the complex number z= 3 - 4i, where a = 3 and b = 4.

The module is

sqrt ( 3^2 + 4^2)

= sqrt ( 9 + 16 )

= sqrt 25

= 5.

**Therefore the module of z = 3 - 4i is 5.**

z = (3-4i). To find the modulus of z.

Modulus of a complex number x+yi = |x+yi| = sqrt(x^2+y^2)

So |z| = |3-4i|

|z)= sqrt {(3^2+(-4)^2}

|z|= sqrt{9+16}

|z) = sqrt25

|z| = 5.

The module of a complex number z = a + i*b is the positive square root of the sum of the squares of the real part, a, and imaginary part, b.

In our case, the complex number is z = 3 - 4i

We'll identify the real part and the imaginary part:

Real part - Re(z) = a

a = 3

Imaginary part - Im(z) = b

b = -4

|z| = sqrt (a^2 + b^2)

|z| = sqrt [3^2+(-4)^2]

|z| = sqrt (9+16)

|z| = sqrt (25)

**|z| = 5**

**The module of the complex number z = 3-4i is |z| = 5.**