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Complex Numbers Introduction

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**What is a complex number?**

A complex number is made up of a real number and an imaginary number. The standard form is a+bi where a is the real term and bi is the imaginary term.

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**Powers of i i = i2 = i3 = i4 = √-1 i i = √-1 √-1 = -1**

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**Practice Simplify i5 = i6 = i7 = i8 =**

Any power of i that is a multiple of 4 is also one. We can find any power of i by writing it as the product of the highest power that is a multiple of 4 and i, i2, and i3.

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More Practice Simplify i25 = i36 = i11 = i19 =

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**Solve quadratic equations with complex roots**

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**Solve quadratic equations with complex roots**

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**Solve quadratic equations with complex roots**

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Practice Page 369 # 17-24, o, o, o, o, 81-92

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**Operations with complex numbers**

Ex. 4 Multiply or divide. Simplify. a.) b.) c.) d.)

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**Operations with complex numbers**

Ex. 5 Write in standard form a+bi.

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**Operations with complex numbers**

Addition & Subtraction (a+bi) + (c+di) = (a+c) + (b+d)i (a+bi) – (c+di) = (a+c) – (b+d)i

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**Operations with complex numbers**

Ex. 6 Find each sum or difference. a.) (4 – 5i) + (-5 + 8i) = b.) (-6 + 3i) + (12 – 9i) = c.) ( i) – (5 – 3i) = d.) (15 – 8i) – ( i) + ( i) =

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**Operations with complex numbers**

Multiplication (a+bi)(c+di) = (ac – bd) + (ad + bc)i FOIL

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**Operations with complex numbers**

Ex. 7 Find each product. a.) (5 + 3i)(2 – 7i) b.) (4 – 5i)2 c.) (3 – i)(-3 + i) d.) (9 – 8i)(9 + 8i)

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**Operations with complex numbers**

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**Operations with complex numbers**

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Practice Page 369 # , 109, 110

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