Respuesta :

emilygooseh

Answer:

i

Step-by-step explanation:

The pattern is as follows

i^1 = i

i^2 = -1

i^3 = -i

i^4 = 1

Following this pattern, i^45 = i.

abidemiokin

The value of the expression [tex]i^{45[/tex] is equal to i

Complex numbers are the square root of negative numbers. For instance:

[tex]\sqrt{-1} = i\\i^2 = -1[/tex]

Given the complex number:

[tex]i^{45}\\= (i^2)^{22} \times i\\= (-1)^{22} \times i[/tex]

Since any value raise to the even values will give a positive value hence;

[tex]=(-1)^{22} \times i\\=1 \times i\\= i[/tex]

This shows that the value of the expression [tex]i^{45[/tex] is equal to i

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