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Minimum value of |z1 + 1 | + |z2 ...

Minimum value of ` |z_1 + 1 | + |z_2 + 1 | + |z _1 z _2 + 1 | if [ z_1 | = 1 and |z_2 | = 1 ` is ________.

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The correct Answer is:
2
`|z_(1) +1|+|z_(1)+1| +|z_(1)z_(2) +1|`
`ge |z_(1) +1| +|z_(2)+1-z_(1)z_(2) -1|`
` ge|z_(1) +1| +|z_(2)||z_(1) -1|`
`=|z_(1) +1| +|z_(1)-1|`
`ge 2`
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