${(1 + i)^{10}}$, where ${i^2} = - 1,$ is equal to
$32\ i$
$64 + i$
$24\ i -32$
None of these
(a) ${(1 + i)^{10}} = {[{(1 + i)^2}]^5} = {(2i)^5} = 32\,i$.
If $\frac{{c + i}}{{c – i}} = a + ib$, where $a,b,c$are real, then ${a^2} + {b^2} = $
If ${\left( {\frac{{1 + i}}{{1 – i}}} \right)^m} = 1,$then the least integral value of $m$ is . . . .
Let the complex number $z=x+$ iy be such that $\frac{2 z-3 i}{2 z+i}$ is purely imaginary. If $x + y ^2=0$, then $y^4+y^2-y$ is equal to :
If $z$ is a complex number satisfying $\left|z^3+z^{-3}\right| \leq 2$, then the maximum possible value of $\left|z+z^{-1}\right|$ is
${i^2} + {i^4} + {i^6} + ……$upto $(2n + 1)$ terms =
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