Presentation on theme: "Multiply complex numbers"— Presentation transcript:
1 Multiply complex numbers Warm-UpMultiply complex numbersWrite the expression as a complex number in standard form.1. 4i(–6 + i)2. (9 – 2i)(–4 + 7i)SOLUTION1. 4i(–6 + i) = –24i + 4i2Distributive property= –24i + 4(–1)Use i2 = –1.= –24i – 4Simplify.= –4 – 24iWrite in standard form.
2 Multiply complex numbers Warm-UpMultiply complex numbers2. (9 – 2i)(–4 + 7i)= – i + 8i – 14i2Multiply using FOIL.= – i – 14(–1)Simplify and use i2 = – 1 .= – i + 14Simplify.= – iWrite 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:.42 - √38 - 4√38 - 4√3===8 - 4√32 + √32 - √34 - 31The conjugate of 2 + √3!
4 Multiply the numerator & denominator by the conjugate! How to…Divide complex numbersGoalNO 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 i ² CANNOT be in the simplified answer! How to…Divide complex numbersi = √-1i ² = -1i ² CANNOT be in the simplified answer!
6 Divide complex numbers Example #1Divide complex numbersWrite the quotient in standard form.7 + 5i1 4i7 + 5i1 – 4i=1 + 4iMultiply numerator and denominator by 1 + 4i, the complex conjugate of 1 – 4i.7 + 28i + 5i + 20i21 + 4i – 4i – 16i2=Multiply using FOIL.7 + 33i + 20(–1)1 – 16(–1)=Simplify and use i2 = 1.– i17=Simplify.
7 Divide complex numbers Example #1Divide complex numbers1317–=+33iWrite in standard form.
8 GUIDED PRACTICEWrite the expression as a complex number in standard form.51 + i1.i(9 – i)3.52–iANSWER1 + 9iANSWER4.5 + 2i2.(3 + i)(5 – i)3 – 2i1113+16iANSWER16 + 2iANSWER
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