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Warm-Up

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

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Warm-Up

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  1. Warm-Up Multiply complex numbers Write the expression as a complex number in standardform. 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.

  2. Warm-Up Multiply complex numbers 2. (9 – 2i)(–4 + 7i) = –36 + 63i + 8i – 14i2 Multiply using FOIL. = –36 + 71i – 14(–1) Simplify and use i2 = – 1 . = –36 + 71i + 14 Simplify. = –22 + 71i Write in standard form.

  3. 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!

  4. 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!

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

  6. 7 + 5i 7 + 5i = 1 – 4i 1 – 4i 1 + 4i 1 + 4i 7 + 28i + 5i + 20i2 = 1 + 4i – 4i – 16i2 7 + 33i + 20(–1) = 1 – 16(–1) –13 + 33i = 17 Example #1 Divide complex numbers 7 + 5i Write the quotient in standard form. 1  4i Multiply numerator and denominator by 1 + 4i, the complex conjugate of 1 – 4i. Multiply using FOIL. Simplify and use i2 = 1. Simplify.

  7. 13 33 – i = + 17 17 Example #1 Divide complex numbers Write in standard form.

  8. 5 11 5 16 5 i i + – 1 + i 13 2 2 13 GUIDED PRACTICE Write the expression as a complex number in standard form. 3. i(9 – i) 1. ANSWER 1 + 9i ANSWER 4. 5 + 2i 2. (3 + i)(5 – i) 3 – 2i ANSWER 16 + 2i ANSWER

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