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 \(\rm z+\frac{2}{z} = 2\).