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3 years ago

Why does the expression i to the power 4n+2 is always equal to -1

Mathematics

1 answer:

Alexandra [31]3 years ago

7 0

Answer:

See Below.

Step-by-step explanation:

We are given:

$i^{4n+2}$

Using exponent properties:

$=i^{4n}\cdot i^2$

Rewriting:

$=(i^4)^n\cdot i^2$

Since i⁴ = 1 and i² = -1:

$=(1)^n\cdot -1$

1 to any power is still 1:

$=1\cdot -1 = -1$

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Two siblings ' ages have a sum of 64 years . The older sibling was born 6 years before their young sibling . Write a system of 2

ELEN [110]

Answer:

younger sibling = 29 years

older sibling = 35 years

Step-by-step explanation:

Let

x = younger sibling

y = older sibling

x + y = 64 (1)

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x = y - 6 (2)

Substitute x = y - 6 into (1)

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y - 6 + y = 64

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3 years ago

The graph of y=3x^2-3x-1 is shown. Use the graph to find estimates for the solutions of i)3x^2-3x+2=2 ii) 3x^2-3x-1=x+1

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Answer:

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Step-by-step explanation:

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$y = 3\cdot x^{2}-3\cdot x +2$

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Now, this system is now represented by means of a graphing tool and whose outcome is attached below. There are two solutions: (0, 2) and (1, 2)

ii) Let be $y=3\cdot x^{2}-3\cdot x -1$ , if $3\cdot x^{2}-3\cdot x +2 = x+1$ , which is equivalent to the following system of equations:

$y = 3\cdot x^{2}-3\cdot x +2$

$y = x+1$

Now, this system is now represented by means of a graphing tool and whose outcome is attached below. There are two solutions: (0.333, 1.333) and (1, 2)

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Why does the expression i to the power 4n+2 is always equal to -1​

Why does the expression i to the power 4n+2 is always equal to -1