Mathematics, 04.07.2019 08:30 pcartei
Correct answers only ! i cannot retake factor the expression completely over the complex numbers. x^4 − 625
Answers: 1
![\text{Use}\\\\a^2-b^2=(a-b)(a+b)\\\\i=\sqrt{-1}\to i^2=-1\\---------------------\\\\x^4-625=(x^2)^2-25^2=(x^2-25)(x^2+25)\\\\=(x^2-5^2)(x^2+5^2)=(x-5)(x+5)[x^2-(-1)(5^2)]\\\\=(x-5)(x+5)[x^2-(i^2)(5^2)]=(x-5)(x+5)[x^2-(5i)^2]\\\\=(x-5)(x+5)(x-5i)(x+5i)](/tpl/images/0049/5963/9742a.png)
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Correct answers only ! i cannot retake factor the expression completely over the complex numbers....
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