In my view the life begins at the time of forming zygote inside the mother's womb. My question is that what is the view of Hinduism about "the beginning of a life"?
Scientifically: You are correct.
By Hinduism: Its a soul,which is going to change a body like clothes, leaving off the old one and wearing newones.see this
vaasaa.nsi jiirNaani yathaa vihaaya navaani gRRihNaati naro.aparaaNi.
tathaa shariiraaNi vihaaya jiirNaanyanyaani sa.nyaati navaani dehii.. B.G. II-22
वासांसि जीर्णानि यथा विहाय नवानि गृह्णाति नरोऽपराणि।
तथा शरीराणि विहाय जीर्णान्यन्यानि संयाति नवानि देही।।
That is: The life of your body begins when Zygote was formed in mother's womb, but there is no life of your soul (and no death either).
Krishna says in the Bhagavad Gita that the soul is eternal i.e. life neither begins nor ends. Ofcourse, the body if formed again and again as mentioned in nobalG's answer.
na tv evaham jatu nasam na tvam neme janadhipah na caiva na bhavisyamah sarve vayam atah param
na—never; tu—but; eva—certainly; aham—I; jātu—become; na—never; āsam—existed; na—it is not so; tvam—yourself; na—not; ime—all these; janādhipāḥ—kings; na—never; ca—also; eva—certainly; na—not like that; bhaviṣyāmaḥ—shall exist; sarve—all of us; vayam—we; ataḥ param—hereafter.
Never was there a time when I did not exist, nor you, nor all these kings; nor in the future shall any of us cease to be.
My SatGuru says human life (i.e., in physical form) starts when the sperm fuses with the Ova. However, it is not that simple.The incoming spirit permeates through both the Ova and the sperm even before they fuse.
Answer is taken from this video: https://www.youtube.com/watch?v=sWXgorb7Ia8