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

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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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