The value of ${(1 + i)^6} + {(1 - i)^6}$ is
$0$
$2^7$
$2^6$
None of these
(a) ${\left( {1 + i} \right)^6} + {(1 – i)^6} = {[{(1 + i)^2}]^3} + {[{(1 – i)^2}]^3}$ $ = \,{(2i)^3} + {( – 2i)^3}$$ = (8 – 8){i^3} = 0$.
For positive integers ${n_1},{n_2}$the value of the expression ${(1 + i)^{{n_1}}} + {(1 + {i^3})^{{n_1}}} + {(1 + {i^5})^{{n_2}}} + {(1 + {i^7})^{{n_2}}}$where $i = \sqrt { – 1} $ is a real number if and only if
Solve the equation $x^{2}-x+2=0$
Solve the equation $x^{2}+3=0$
Let the minimum value $v_{0}$ of $v=|=|^{2}+|z-3|^{2}+|z-60|^{2}$, $z \in C$ is attained at $z=z_{0}$. Then $\left|2 z_{0}^{2}-z_{0}^{3}+3\right|^{2}+v_{0}^{2}$ is equal to.
Let $\quad S=\left\{z \in C-\{i, 2 i\}: \frac{z^2+8 i z-15}{z^2-3 i z-2} \in R \right\}$. $\alpha-\frac{13}{11} i \in S , \alpha \in R -\{0\}$, then $242 \alpha^2$ is equal to
