How can you simplify $$i^{1025}$$ ?

Since $$1025 mod 4 = 1$$ , $$i^{1025} = i$$ .

What is the value of $$i^{10}$$ ?

Since $$10 mod 4 = 2$$ , $$i^{10} = i^2 = -1$$ .

What is the value of $$i^{15}$$ ?

Since $$15 mod 4 = 3$$ , $$i^{15} = i^3 = -i$$ .

What is the value of $$i^{20}$$ ?

Since $$20 mod 4 = 0$$ , $$i^{20} = i^0 = 1$$ .

What is the value of $$i^{-1}$$ ?

$$i^{-1} = \frac{1}{i} = -i$$ (after multiplying by $$\frac{i}{i}$$ ).

What is the value of $$i^{-2}$$ ?

$$i^{-2} = \frac{1}{i^2} = -1$$ .

What is the value of $$i^{-3}$$ ?

$$i^{-3} = \frac{1}{i^3} = \frac{1}{-i} = i$$ (after multiplying by $$\frac{i}{i}$$ ).

What is the value of $$i^{-4}$$ ?

$$i^{-4} = \frac{1}{i^4} = 1$$ .

What is the significance of the imaginary unit i in complex numbers?

i is defined as $$i = \text{sqrt}(-1)$$ and is used to extend the real number system to complex numbers.

How do you express a complex number using i?

A complex number is expressed as $$a + bi$$ , where $$a$$ is the real part and $$b$$ is the imaginary part.

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Math

Algebra

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Exit Ticket Powers Of I

Exit Ticket - Powers of i

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Mathematics

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11th Grade

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Practice Problem

•

Hard

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FLASHCARD QUESTION

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FLASHCARD QUESTION

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-1

FLASHCARD QUESTION

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-i

FLASHCARD QUESTION

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FLASHCARD QUESTION

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What is the pattern in the powers of i?

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The powers of i cycle every four: i, -1, -i, 1.

FLASHCARD QUESTION

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FLASHCARD QUESTION

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