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Determine the product of -1-i√2 and its conjugate.a. -1-2i√2.  b. -1+2i√2 c....

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melissazamora7 | Student, Grade 11 | Honors

Posted September 9, 2012 at 7:22 PM via web

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Determine the product of -1-i√2 and its conjugate.

a. -1-2i√2. 

b. -1+2i√2

c. -3

d. 3

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lfryerda | High School Teacher | (Level 2) Educator

Posted September 9, 2012 at 8:46 PM (Answer #1)

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Consider the complex number `a+ib` and its conjugate `a-ib` .  Then its product is:

`(a+ib)(a-ib)`

`=a^2+iab-iab-i^2b^2`

`=a^2+b^2`

So for the number `-1-isqrt2` , the product of it and its conjugate is

`(-1)^2+(-sqrt2)^2`

`=1+2`

`=3`

The product is answer d and is 3.

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