NCERT Exemplar Solutions
Class 11 - Mathematics - Chapter 5: COMPLEX NUMBERS AND QUADRATIC EQUATIONS

Fill in the Blanks

(i) For any two complex numbers \(z_1, z_2\) and any real numbers \(a, b\), \(\; |az_1 - bz_2|^2 + |bz_1 + az_2|^2 = ____\).

(ii) The value of \(\sqrt{-25} \times \sqrt{-9}\) is ____.

(iii) The number \(\dfrac{(1 - i)^3}{1 - i^3}\) is equal to ____.

(iv) The sum of the series \(i + i^2 + i^3 + \dots\) up to 100 terms is ____.

(v) The multiplicative inverse of \(1 + i\) is ____.

(vi) If \(z_1\) and \(z_2\) are complex numbers such that \(z_1 + z_2\) is a real number, then \(z_2 = ____\).

(vii) \(\arg(z) + \arg(\overline{z})\) \((\overline{z} \ne 0)\) is ____.

(viii) If \(|z + 4| \le 3\), then the greatest and least values of \(|z + 1|\) are ____ and ____ respectively.

(ix) If \(\left|\dfrac{z - 2}{z + 2}\right| = \dfrac{\pi}{6}\), then the locus of \(z\) is ____.

(x) If \(|z| = 4\) and \(\arg(z) = \dfrac{5\pi}{6}\), then \(z = ____\).