Operations with Imaginary Numbers

Why do we get imaginary numbers?

• When a square root has a positive on the outside

  $3x^2\sqrt{14x}$

• When a square root has a negative on the outside $-3x^2\sqrt{14x}$

• When a square root has a positive on the inside $\sqrt{14}$

• When a square root has a negative on the inside $\sqrt{-14}$

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CCSS.HSN.CN.A.1

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Using your calculator, evaluate i¹³

• -1

• 1

• i

• -i

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CCSS.HSN.CN.A.1

CCSS.HSN.CN.A.2

Using your calculator, evaluate i^24

• -1

• 1

• i

• -i

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CCSS.HSN.CN.A.1

CCSS.HSN.CN.A.2

Using your calculator, evaluate i⁷

• -1

• 1

• i

• -i

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CCSS.HSN.CN.A.1

CCSS.HSN.CN.A.2

Using your calculator, evaluate i²

• -1

• 1

• i

• -i

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CCSS.HSN.CN.A.1

CCSS.HSN.CN.A.2

What is the simplified form of (–9 + 5i) + (3 – 2i)

*Your calculator can do problems 6 through 8 :)

• –12 + 31i

• –6 + 3i

• –11 + 7i

• 5 – 3i

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CCSS.HSN.CN.A.1

CCSS.HSN.CN.A.2

What is the simplifies form of (11 – 7i) – (–3 + 12i)

• 8 – 19i

• 8 + 5i

• 13 – 19i

• 14 –19i

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CCSS.HSN.CN.A.1

CCSS.HSN.CN.A.2

What is the simplified form of (–6i)(3i)

• –18

• –18i

• 18

• –18i²

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CCSS.HSN.CN.A.1

CCSS.HSN.CN.A.2

What is the simplified form of (–3x + 2i)(x– 4i)

• –3x² + 6xi – 8

• –3x² + 6xi + 8

• –3x² + 14xi – 8

• –3x² + 14xi + 8

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CCSS.HSN.CN.A.1

CCSS.HSN.CN.A.2

(5x – 2i) + (–7x + 8i)

• –2x + 6i

• 12x + 6i

• –35x – 16i²

• –35 – 16i

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CCSS.HSN.CN.A.1

CCSS.HSN.CN.A.2