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4-1.Complex numbers
normal
જો $z$ એ સંકર સંખ્યા હોય, તો $z.\,\overline z = 0$ થવા માટે . . . .
A
$z = 0$
B
${\mathop{\rm Re}\nolimits} (z) = 0$
C
${\mathop{\rm Im}\nolimits} \,(z) = 0$
D
એકપણ નહીં.
Solution
(a)Let $z = x + iy,\overline z = x – iy$
$\therefore $ $z\overline z = 0$
==> $(x + iy)(x – iy) = 0$
==> ${x^2} + {y^2} = 0$
It is possible only when $x$ and $y$both simultaneously zero i.e., $z = 0 + 0i = 0$
Standard 11
Mathematics
