Question

The module of complex number 2+i root 3 is??​

Answer 1

Answer:

√7

Step-by-step explanation:

The modulus of a+bi is √(a²+b²).

So the modulus of 2+i√3 is

√( 2² + √3²) = √( 4 + 3 ) = √7

Answer 2

Given:

2+i root 3

To Find:

The module of a complex number

Solution:

A complex number is a combination of imaginary number and real number, where the imaginary number has a coefficient of a real number and it is overall expressed in the form a+bi,

The modulus of a complex number is represented by |z|, and the formula for the same is,

$z=a+ib\\|z|=\sqrt{a^2+b^2}$

Now we are given a complex number,

$z=2+i\sqrt{3}$

Now the modulus of the given complex number using the stated formula will be,

$|z|=\sqrt{2^2+\sqrt{3}^2 }\\ =\sqrt{4+3}\\ =\sqrt{7}$

Hence, the modulus of 2+i root 3 is root 7.