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**Multiply complex numbers**

Warm-Up Multiply complex numbers Write the expression as a complex number in standard form. 1. 4i(–6 + i) 2. (9 – 2i)(–4 + 7i) SOLUTION 1. 4i(–6 + i) = –24i + 4i2 Distributive property = –24i + 4(–1) Use i2 = –1. = –24i – 4 Simplify. = –4 – 24i Write in standard form.

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**Multiply complex numbers**

Warm-Up Multiply complex numbers 2. (9 – 2i)(–4 + 7i) = – i + 8i – 14i2 Multiply using FOIL. = – i – 14(–1) Simplify and use i2 = – 1 . = – i + 14 Simplify. = – i Write in standard form.

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**. How to… Divide complex numbers**

Remember when we needed to divide radical expressions in Math 1?? How did we do that?!?! As a refresher, how would you divide the following: . 4 2 - √3 8 - 4√3 8 - 4√3 = = = 8 - 4√3 2 + √3 2 - √3 4 - 3 1 The conjugate of 2 + √3!

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**Multiply the numerator & denominator by the conjugate!**

How to… Divide complex numbers Goal NO IMAGINARY NUMBERS IN THE DENOMINATOR!! Multiply the numerator & denominator by the conjugate! (a + bi) has a conjugate of (a – bi) and (a – bi) has a conjugate of (a + bi) Then complete your steps for multiplying complex numbers!

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**i ² CANNOT be in the simplified answer!**

How to… Divide complex numbers i = √-1 i ² = -1 i ² CANNOT be in the simplified answer!

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**Divide complex numbers**

Example #1 Divide complex numbers Write the quotient in standard form. 7 + 5i 1 4i 7 + 5i 1 – 4i = 1 + 4i Multiply numerator and denominator by 1 + 4i, the complex conjugate of 1 – 4i. 7 + 28i + 5i + 20i2 1 + 4i – 4i – 16i2 = Multiply using FOIL. 7 + 33i + 20(–1) 1 – 16(–1) = Simplify and use i2 = 1. – i 17 = Simplify.

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**Divide complex numbers**

Example #1 Divide complex numbers 13 17 – = + 33 i Write in standard form.

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GUIDED PRACTICE Write the expression as a complex number in standard form. 5 1 + i 1. i(9 – i) 3. 5 2 – i ANSWER 1 + 9i ANSWER 4. 5 + 2i 2. (3 + i)(5 – i) 3 – 2i 11 13 + 16 i ANSWER 16 + 2i ANSWER

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M3U3D4 Warm Up Divide using Synthetic division: (2x ³ - 5x² + 3x + 7) /(x - 2) 2x² - x + 1 + 9/(x-2)

M3U3D4 Warm Up Divide using Synthetic division: (2x ³ - 5x² + 3x + 7) /(x - 2) 2x² - x + 1 + 9/(x-2)

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