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

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