Download App

Complex Numbers — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsComplex Numbers3 Marks
Question
Show that $1+\text{i}^{10}+\text{i}^{20}+\text{i}^{30}$ is a real number.
✓

Answer

$1+\text{i}^{10}+\text{i}^{20}+\text{i}^{30}=1+\text{i}^{4\times2}\times\text{i}^2+\text{i}^{4\times5}+\text{i}^{4\times7}\times\text{i}^2$ $=1+1\times\text{i}^2+1+1\times\text{i}^2$ $=1-1+1-1$$=0,$ which is real number.

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 "3 Marks Question" from Complex Numbers→Complex Numbers — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Find the equation of the straight line at a distance of 3 units from the origin such that the perpendicular from the origin to the line makes an angle $\tan^{-1}\Big(\frac{5}{12}\Big)$ with the positive direction of x-axis.
→
In a school there are 20 teachers who teach mathematics or physics. Of these, 12 teach mathematics and 4 physics and mathematics. How many teach physics?
→
box contains $6$ red marbles numbered $1$ through $6$ and $4$ white marble numbered form $12$ through $15$. find the probability that a marble drawn is:
  1. White
  2. White and odd numbered
  3. Even numbered
  4. Red or even numbered.
→
A bag contains six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag if:
  1. They can be of any colour.
  2. Two must be white and two red and.
  3. They must all be of the same colour.
→
In shuffling a pack of 52 playing cards, form four are accidently dropped; find the missing cards should be one form each suit.
→
Expand the given expression $(2x - 3)^6$
→
By using the concept of equation of a line, prove that the three points $(3, 0), (-2, -2)$ and $(8, 2)$ are collinear.
→
Find what the following equations become when the origin is shifted to the point $(1, 1)$?
$x^2 + xy − 3x − y + 2 = 0$
→
Let f(x) be a function defined by $\text{f(x)}=\begin{cases}\frac{3\text{x}}{|\text{x}|+2\text{x}}, & \text{x} \neq0\\\ \ \ \ 0, & \text{x} = 0\end{cases}.$
→
If the $4^{th}, 10^{th} $ and $16^{th} $ terms of a G.P. are $x, y$ and $z$ respectively. Prove that $x, y , z$ are in G.P.
→