1 + {i^2} + {i^4} + {i^6} + ..... + {i^{2n}} is

English

Gujarati

Hindi

4-1.Complex numbers

medium

$1 + {i^2} + {i^4} + {i^6} + ..... + {i^{2n}}$is

Positive

Negative

Zero

Cannot be determined

Solution

(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.

Standard 11

Mathematics

Solve the equation $2 x^{2}+x+1=0$

medium

If $\left| {z – 3 + 2i} \right| \leq 4$ then the difference between the greatest value and the least value of $\left| z \right|$ is

hard

(JEE MAIN-2018)

If $z(1 + a) = b + ic$ and ${a^2} + {b^2} + {c^2} = 1$, then $\frac{{1 + iz}}{{1 – iz}} = $

medium

If $4 x+i(3 x-y)=3+i(-6),$ where $x$ and $y$ are real numbers, then find the values of $x$ and $y.$

easy

If $n$ is a positive integer, then which of the following relations is false

easy

$1 + {i^2} + {i^4} + {i^6} + ..... + {i^{2n}}$is

Solution

Similar Questions

Solve the equation $2 x^{2}+x+1=0$

If $\left| {z – 3 + 2i} \right| \leq 4$ then the difference between the greatest value and the least value of $\left| z \right|$ is

If $z(1 + a) = b + ic$ and ${a^2} + {b^2} + {c^2} = 1$, then $\frac{{1 + iz}}{{1 – iz}} = $

If $4 x+i(3 x-y)=3+i(-6),$ where $x$ and $y$ are real numbers, then find the values of $x$ and $y.$

If $n$ is a positive integer, then which of the following relations is false

Start a Free Trial Now