Question

Find absolute values of $2 + 5i$?

Answer 1

Hint:In the given question, we are required to find the absolute value of the given complex number. The absolute value of a complex number is also known as the modulus of the complex number. The modulus of a complex number represents the distance of the point represented by the complex number on the Argand plane from the origin.

Complete step by step solution:
Consider the given complex number in standard form as$x + iy$.
Let it be represented by Z.
So, $Z = x + iy = 2 + 5i$.
On comparing real part and imaginary part of both left and right sides of the equation, we get the values of x and y as:
$x = 2$ and $y = 5$
The absolute value of a complex number is given by $\left| Z \right|$ and it is calculated as:
$\left| Z \right| = \sqrt {{x^2} + {y^2}} $
Thus, putting in the values of x and y, we get the absolute value of given complex number as:
$\left| Z \right| = \sqrt {{{(2)}^2} + {{(5)}^2}} $
$ \Rightarrow \left| Z \right| = \sqrt {29} $
So, the absolute value of the given complex number $2 + 5i$ is $\left( {\sqrt {29} } \right)$.

Note: The modulus of a complex number is the same as the absolute value of the complex number. We can find the absolute value of a complex number by first comparing the real and imaginary parts of the complex numbers and then putting the values of both real and imaginary parts in the formula of modulus or absolute value of complex numbers.