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ANTONII [103]
3 years ago
13

What is the value of i^n in if the remainder of n/4 is 2?

Mathematics
2 answers:
LekaFEV [45]3 years ago
5 0

The value of {i^n} is \boxed{ - 1} if the remainder of \dfrac{n}{4} is 2.

Further Explanation:

Given:

The remainder of \dfrac{n}{4} is 2.

Explanation:

The sum of imaginary numbers and real numbers is known as the complex number.

The complex number can be expressed as follows,

\boxed{z = a + ib}

Here, a is the real part of the complex number and \text{ib} is the imaginary part of the complex number.

\sqrt{ - 1} can be denoted by i.

The value of {i^2} is -1.

{i^2} =  - 1

The value {i^3} can be obtained as follows,

\begin{aligned}{i^3}&= {i^2} \times i\\&= - 1 \times i \\&= - i\\\end{aligned}

The value {i^4} can be obtained as follows,

\begin{aligned}{i^4} &= {i^2} \times {i^2}\\&= - 1 \times - 1 \\&= 1\\\end{aligned}

The value of {i^n} is \boxed{ - 1} if the remainder of \dfrac{n}{4} is 2.

Learn more:

  1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
  2. Learn more about equation of circle brainly.com/question/1506955.
  3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Complex numbers

Keywords: value, i^ n, remainder, n/4, 2 quotient, divisor, complex number, imaginary number, real number, exponents, dividend, powers, -1, imaginary roots.

Anastasy [175]3 years ago
5 0

i² = -1

_____

i⁰ = 1

i¹ = i

i² = -1

i³ = -i

and then the pattern repeats

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