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Published byElisa Blackledge Modified over 2 years ago

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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 + 4i 2 Distributive property = –24i + 4(–1) Use i 2 = –1. = –24i – 4 Simplify. = –4 – 24i Write in standard form.

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Warm-Up Multiply complex numbers 2. (9 – 2i)(–4 + 7i) Multiply using FOIL. = – i + 8i – 14i 2 = – i – 14(–1) Simplify and use i 2 = – 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: = = = 1 The conjugate of 2 + 3!

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

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

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Example #1 Divide complex numbers Write the quotient in standard form i 1 4i 7 + 5i 1 – 4i 7 + 5i 1 – 4i = 1 + 4i Multiply numerator and denominator by 1 + 4i, the complex conjugate of 1 – 4i i + 5i + 20i i – 4i – 16i 2 = Multiply using FOIL i + 20(–1) 1 – 16(–1) = Simplify and use i 2 = 1. – i 17 = Simplify.

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Example #1 Divide complex numbers – = i Write in standard form.

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

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