Question

simplify i^2020 + i^2020

challenge question please answer and it's urgent!​

Answer 1

We have to simplify the given expression :-

$\longrightarrow \rm \large{i}^{2020} + {i}^{2020} \\ \\ \rm \: where \: \: i = \sqrt{ - 1} \\ \\ \longrightarrow \rm \large{( {i}^{2} )}^{1010} + { ({i}^{2}) }^{1010} \\ \\ \\ \longrightarrow \rm \large{( {i}^{2} )}^{1010} + { ({i}^{2}) }^{1010} \\ \\ \\ \rm we \: know \: that :\rightarrow \: { {i}^{2} } = - 1\\ \\ \\ \longrightarrow \rm \large{( - 1)}^{1010} + { ( - 1) }^{1010}\\ \\ \\ \longrightarrow \rm \large1 + 1\\ \\ \\ \longrightarrow \rm \large2$

Answer :- 2

Additional Information :-

Properties of Modules :-

If X = a+bi then ,

1) | X | = |- X |

2) | X₁ X₂ | = | X₁ | | X₂ |

3) | X₁ / X₂ | = | X₁ | / | X₂ |

4) | X₁ + X₂ | ≠ | X₁ | + | X₂ |

Properties of argument :-

1) Arg(0) = not defined

2) If X is purely imaginary number then , arg(X) = ± (π/2)

3) Arg( X₁ X₂) = Arg( X₁ ) + Arg( X₂) + 2mπ

4) Arg( X₁ - X₂) = Arg( X₁ ) - Arg( X₂) + 2mπ

5) Arg( Xⁿ) = n Arg( Xⁿ) + 2mπ