Download App

4.1 complex nubers — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS4.1 complex nubers1 Mark
MCQ
$1 + {i^2} + {i^4} + {i^6} + ..... + {i^{2n}}$is
  • A
    Positive
  • B
    Negative
  • C
    Zero
  • ✓
    Cannot be determined
✓

Answer

Correct option: D.
Cannot be determined
d
(d) $S = 1 + {i^2} + {i^4} + ..... + {i^{2n}} = 1 - 1 + 1 - 1 + ...... + {( - 1)^n}$
Obviously it depends on $n$.
Hence cannot be determined unless $n$ is known.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from 4.1 complex nubers→4.1 complex nubers — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\omega $ is an imaginary cube root of unity, ${(1 + \omega - {\omega ^2})^7}$equals
→
$\mathop {\lim }\limits_{x \to 2} \frac{{|x - 2|}}{{x - 2}} = $
→
$\mathop {\lim }\limits_{x \to 0} \frac{{x\tan 2x - 2x\tan x}}{{{{(1 - \cos 2x)}^2}}}$ is
→
The smallest positive root of the equation $tanx\,  -\,  x = 0$ lies on
→
Let $PS$ be the median of the triangle with vertices $P(2,2) , Q(6,-1) $ and $R(7,3) $. The equation of the line passing through $(1,-1) $ and parallel to $PS $ is :
→
If for real values of $x,\cos \theta = x + \frac{1}{x},$ then
→
Statement $1$ : The variance of first $n$ odd natural numbers is $\frac{{{n^2} - 1}}{3}$
Statement $2$ : The sum of first $n$ odd natural number is $n^2$ and the sum of square of first $n$ odd natural numbers is $\frac{{n\left( {4{n^2} + 1} \right)}}{3}$
→
If $\cos \,\left( {\alpha  + \beta } \right) = \frac{3}{5},\,\sin \,\left( {\alpha  - \beta } \right) = \frac{5}{{13}}$ and $0 < \alpha ,\beta  < \frac{\pi }{4}$ then $\tan \,\left( {2\alpha } \right)$ is equal to
→
Tangents are drawn from the point $(17,7)$ to the circle $x^2+y^2=169$.

$STATEMENT -1$ : The tangents are mutually perpendicular. because

$STATEMENT - 2$ : The locus of the points from which mutually perpendicular tangents can be drawn to the given circle is $x^2+y^2=338$

→
Four persons independently solve a certain problem correctly with probabilities $\frac{1}{2}, \frac{3}{4}, \frac{1}{4}, \frac{1}{8}$. Then the probability that the problem is solved correctly by at least one of them is
→