Question

Find the modulus of complex number z =2-i

Answer 1

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Given ,

The Complex number (z) is 2 - i

Real part of z (a) = 2

Imaginary part of z (b) = -1

We know that , The modulus of z is given by

$\large \mathtt{ \fbox{r = \sqrt{ {(a)}^{2} + {(b)}^{2} } } }$

Where ,

a = real part of complex number

b = imaginary part of complex number

Substitute the known values , we obtain

$\sf \hookrightarrow Modulus \: of \: z \: (r) = \sqrt{ {(2)}^{2} + {( - 1)}^{2} } \\ \\\sf \hookrightarrow Modulus \: of \: z \: (r) = \sqrt{4 + 1} \\ \\\sf \hookrightarrow Modulus \: of \: z \: (r) = \sqrt{5}$

Hence , the modulus of given complex number is √5