At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Experience the ease of finding quick and accurate answers to your questions from professionals on our platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
Consider the given expression,
[tex]x^2+2x+2[/tex]Consider the properties,
[tex]\begin{gathered} i^2=-1 \\ i^3=-i \\ i^4=1 \end{gathered}[/tex]Let us check each expression, and the one which upon simplification gives the identical quadratic expression will be the correct choice.
Solve the first option,
[tex]\begin{gathered} (x-1+i)(x-1-i) \\ =(x-1)^2-(i)^2 \\ =(x^2-2x+1)-(-1) \\ =x^2-2x+1+1 \\ =x^2-2x+2 \end{gathered}[/tex]Since this is not identical to the given quadratic polynomial, first option is incorrect.
Solve the second option,
[tex]\begin{gathered} (x+2(x+1) \\ =x(x+1)+2(x+1) \\ =x^2+x+2x+2 \\ =x^2+3x+2 \end{gathered}[/tex]Since this is not identical to the given quadratic polynomial, second option is incorrect.
Solve the third option,
[tex]\begin{gathered} (x+1-i)(x+1+i) \\ =(x+1)^2-(i)^2 \\ =(x^2+2x+1)-(-1) \\ =x^2+2x+1+1 \\ =x^2+2x+2 \end{gathered}[/tex]Since this is identical to the given quadratic polynomial, third option is incorrect.
Thus, the third expression is equivalent to the given quadratic polynomial.
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.
