If n , then find the value of i^n+i^ n+1 +i^ n+2 +i^ n+3 . - Vidyadip

Question

If $\text{n}\in\text{N},$ then find the value of $\text{i}^\text{n}+\text{i}^{\text{n}+1}+\text{i}^{\text{n}+2}+\text{i}^{\text{n}+3}.$

✓

Answer

$\text{i}^\text{n}+\text{i}^{\text{n}+1}+\text{i}^{\text{n}+2}+\text{i}^{\text{n}+3}$ $=\text{i}^\text{n}+\text{i}^{\text{n}}.\text{i}+\text{i}^{\text{n}}.\text{i}^2+\text{i}^{\text{n}}.\text{i}^3$ $=\text{i}^\text{n}+\text{i}^{\text{n}}.\text{i}+\text{i}^{\text{n}}.(-1)+\text{i}^{\text{n}}.(-\text{i})$ $=\text{i}^\text{n}+\text{i}^{\text{n}}.\text{i}-\text{i}^{\text{n}}-\text{i}^{\text{n}}.\text{i}$ $=0$ Thus, the value of $\text{i}^\text{n}+\text{i}^{\text{n}+1}+\text{i}^{\text{n}+2}+\text{i}^{\text{n}+3}$ is 0.

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 "(Each question 1 marks)" from Complex Numbers→Complex Numbers — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The given following sets are finite & in which of it infinite in if? Set of letters of the English Alphabets;

Find the degree measure to the radian measure $\left( {use\;\pi \frac{{22}}{7}} \right)\frac{{11}}{{16}}$

Write the sum of the series $1^2 - 2^2 + 3^2 - 4^2 + 5^2 - 6^2 + ..... + (2n - 1)^2 - (2n)^2$

Answer each of the following questions in one word or sentence or as per exact requirement of the question write the eccentricity of the hyperbola $9\text{x}^{2}-16\text{y}^{2}=144$

If A = {1, 2, 3}, B = {4, 5, 6}, the given following are relations from A to B? Give reason in support of your answer.{(4, 2), (4, 3), (5, 1)}

Which of the following statements are true and which are false? In each case give a valid reason for saying so: s: If x and y are integers such that x > y, then -x < -y.

Which of the following sentences are statements? Give reasons for your answer. Mathematics is difficult.

Write the maximum number of points of intersection of 8 straight lines in a plane.

If A is any set, prove that: $\text{A}\subseteq\phi\Leftrightarrow\text{A}=\phi.$

If $\frac{\pi}{2}<\text{x}<\pi,$ then find $\frac{\text{d}}{\text{dx}}\Bigg(\sqrt{\frac{1+\cos\text{2x}}{2}}\Bigg)$