Question

what is the value of i^2021 ​

Answer 1

Value of $\bf {i}^{2021}$ is $\bf i$.

Given: ${i}^{2021}$

To find: Value of above written expression.

Solution:

We know that, √-1 is an imaginary number and it can be expressed as 'i' pronounced as 'iota'.

Therefore

${i}^{2} = - 1 \\ {i}^{3} = - i \\ {i}^{4} = 1$

i.e. all the multiples of 4 in power of iota turns to 1.

Step 1: Write power of iota in terms of multiple of 4.

${i}^{2021} = {i}^{2020} \times i$

as

$\because \bf {a}^{n + m} = {a}^{n} \times {a}^{m}$

or

${i}^{2021} = {i}^{4(505)} \times i$

Step 2: Place value of i⁴.

${i}^{2021} = ( {i}^{4})^{(505)} \times i$

${i}^{2021} = (1)^{(505)} \times i$

$\because \bf {a}^{nm} = {a}^{n^{m}}$

${i}^{2021} = 1 \times i$

$\bf {i}^{2021} = i$

Therefore,

Value of ${i}^{2021}$ is i.

Learn more:

What is the value of the [i^19+(1÷i)^25]^2

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प्रश्न 1 से 10 तक की सम्मिश्र संख्याओं मे प्रत्येक को a +ib के रूप य व्यक्त कीजिए l $\iota^{-39}$

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