- Home
- Standard 11
- Mathematics
4-1.Complex numbers
easy
यदि $z \ne 0$ एक सम्मिश्र संख्या हो, तो
A
${\mathop{\rm Re}\nolimits} (z) = 0 \Rightarrow {\mathop{\rm Im}\nolimits} ({z^2}) = 0$
B
${\mathop{\rm Re}\nolimits} ({z^2}) = 0 \Rightarrow {\mathop{\rm Im}\nolimits} ({z^2}) = 0$
C
${\mathop{\rm Re}\nolimits} (z) = 0 \Rightarrow {\mathop{\rm Re}\nolimits} ({z^2}) = 0$
D
इनमें से कोई नहीं
Solution
(a) यदि $z \ne 0$. माना $z = x + iy$ $⇒ {z^2} = {x^2} – {y^2} + i(2xy)$
$Re(z)= 0 ⇒ x = 0$. इसलिए ${\mathop{\rm Im}\nolimits} ({z^2}) = 2xy = 0$
अत: ${\mathop{\rm Re}\nolimits} (z) = 0 \Rightarrow {\mathop{\rm Im}\nolimits} ({z^2}) = 0$.
Standard 11
Mathematics
