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Perform the operation and get your answer in the form a + bi.   (3 + 2i)(2 - 4i)

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kristenmarieb... | Student, Grade 10 | (Level 1) Valedictorian

Posted April 13, 2013 at 3:22 AM via web

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Perform the operation and get your answer in the form a + bi.

 

(3 + 2i)(2 - 4i)

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violy | High School Teacher | (Level 3) Assistant Educator

Posted April 13, 2013 at 3:27 AM (Answer #1)

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Use foil method. 

First terms: 3 * 2 = 6. 

Outer terms: 3*-4i = -12i

Inner terms: 2i*2 = 4i

Last terms: 2i*-4i = -8i^2

So, we will have:(3 + 2i)(2 - 4i) = 6 - 12i + 4i - 8i^2 

Combine like terms, and take note that i^2 = -1. 

6 - 12i + 4i - 8i^2 = 6 - 8i -8(-1) = 6 - 8i + 8 = 14 - 8i

Therefore, final answer is 14 - 8i.

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rakesh05 | High School Teacher | (Level 1) Assistant Educator

Posted April 13, 2013 at 5:51 AM (Answer #3)

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`(3+2i)(2-4i)=(3.2-3.4i+2i.2-2i.4i)`

                          `=(6-12i+4i-8i^2)`

                          `=(6-8i-8.(-1))`       Since `i^2=-1`

                          `=(6-8i+8)`

                         `=(14-8i)` .      Answer.

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