Back to all chapters
# Complex Numbers

"Complex" numbers share many properties with the real numbers. In fact, complex numbers include all the real numbers, so you know lots of them already. Such an overachiever.

If \[ x (x-4-9i)(x-a+bi) = x^3 -8x^2+97x, \] what is \( a + b \) ?

**Details and assumptions**

\( i \) is the the imaginary unit, defined by \( i^2 = -1 \).

Suppose that \[\begin{align} & x^4+6x^3+17x^2-6x-18 \\ &= (x+a)(x-a)(x+b+ci)(x+b-ci), \end{align} \] where \(i\) is the imaginary number that satisfies \(i^2=-1\). What is the value of \(a+b+c\)?

**Details and assumptions**

Assume \( a > 0 \) and \( c > 0 \).

×

Problem Loading...

Note Loading...

Set Loading...