Question

Find the modulus of the complex number 2 — 5i.

Answer 1

Hint: In these types of questions always remember the basic formula of modulus. If complex number is given as a + ib then modulus of a complex number=$|Z| = \sqrt {{a^2} + {b^2}}$. Use this formula to get the required answer.

Complete step-by-step answer:
Here we have a complex number whose value is 2 — 5i
Let Z= 2— 5i ---(equation 1)
On comparing with general form a=2 and b=(-5).
Now let’s use the basic formula of finding a modulus of a complex number=$|Z| = \sqrt {{a^2} + {b^2}}$
$\Rightarrow$ |Z|=$\sqrt {{{(2)}^2} + {{( - 5)}^2}}$
$\Rightarrow$ |Z|=$\sqrt {4 + 25}$
$\Rightarrow$ |Z|=$\sqrt {29}$
Hence $\sqrt {29}$ is the modulus of the complex number 2 — 5i.

Note: In these types of questions first identify the a and b in the complex number then use the basic formula of finding the modulus of the complex number i.e. $|Z| = \sqrt {{a^2} + {b^2}}$ and put the correct values in the formula for finding the modulus and simplify the value of modulus.