Question

Find the modulus of the complex number \(\rm 2i +1\over 2 + i\).
1. 1
2. -1
3. 2
4. -2

Answer 1

Correct Answer - Option 1 : 1

Concept;

Modulus of a complex number z = x + iy

|z| = \(\rm \sqrt{x^2 + y^2}\)

Calculation:

Let z = \(\rm 2i +1\over 2 + i\)

Multiplying by the conjugate of the denominator

z = \(\rm {2i +1\over 2 + i}\times {2-i\over 2-i}\)

z = \(\rm 4i + 2 + 2 -i\over 4-(-1)\)

z = \(\rm 3i +4\over 5\)

Now magnitude of z

|z| = \(\sqrt{{\left(3\over 5\right)}^2+ {\left(4\over 5\right)}^2}\)

|z| = \(\sqrt {\left(9+16\over2 5\right)}\)

|z| = 1