# If Z = 1 + i, where i = √-1, then what is the modulus of $\rm z+\frac{2}{z}?$

43 views

closed
If Z = 1 + i, where i = √-1, then what is the modulus of $\rm z+\frac{2}{z}?$
1. 1
2. 2
3. 3
4. 4

by (54.3k points)
selected

Correct Answer - Option 2 : 2

Concept:

i2 = -1

Calculation:

Given z = 1 + i

We have to find the modulus of z + $\rm \frac{2}{Z}$

⇒ (1 + i) + $\rm \frac{2}{1 + i}$

On rationalizing the second term, we get

(1 + i)$\rm \frac{2}{1 + i}$$\times$$\rm \frac{1 - i}{1 - i}$

(1 + i)$\rm \frac{2\times (1 - i)}{1 - i^{2}}$

(1 + i)$\rm \frac{2\times (1 - i)}{1 - (-1)}$

(1 + i)$\rm \frac{2\times (1 - i)}{2}$

1 + i + 1 - i

2

∴ The modulus of $\rm z+\frac{2}{z} = 2$.