[size=150] Select [b]all[/b] the expressions that are equivalent to [math](3-5i)(\text{-}8+2i)[/math][/size]

[size=150]Explain or show how to write [math](20-i)(8+4i)[/math] in the form [math]a+bi[/math], where [math]a[/math] and [math]b[/math] are real numbers.[/size]

[math](\text{-}9+2i)(10-13i)=\text{-}68-97i[/math]

[math](\hspace{1cm} - 2i)(\hspace{1cm} + 2i) = \hspace{1cm} - 10i[/math][br]What could go in the blanks?[br]

Could other numbers work, or is this the only possibility? Explain your reasoning.[br]

[math]x^2=49[/math]

[math]x^3=49[/math]

[math]x^2=\text{-}49[/math]

[math]x^3=\text{-}49[/math]

Optionally, plot [math]3+2i[/math] in the complex plane. Then plot and label each of your answers.[br][list][*][math]2(3+2i)[/math][/*][*][math]i(3+2i)[/math][/*][*][math]\text{-}i(3+2i)[/math][/*][*][math](3-2i)(3+2i)[/math][/*][/list]

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[/img][br]Describe a pattern in how each account balance changed from one year to the next.[br]

Define the amount of money, in thousands of dollars, in accounts [math]A[/math] and [math]B[/math] as functions of time [math]t[/math], where [math]t[/math] is years since 2000, using function notation.[br]

Will account [math]A[/math] ever have the same balance as account [math]B[/math]? If so, when? Explain how you know.[br]