9.7 Sample test: complex numbers

Fill in the following table.

$(i{)}^{85}=$

$(5i{)}^2=$

$(ni{)}^{103}=$

• A

  $\sqrt{-\text{20}}$ =

• B

  Other than your answer to part (a), is there any other number that you can squareto get –20? If so, what is it?

$(3w–zi{)}^2=$

• A

  Complex conjugate of $4+i=$

• B

  What do you get when you multiply $4+i$ by its complex conjugate?

$\mathrm{–i}$

• A

  $a=$

• B

  $b=$

$\frac{n}{i}$

• A

  $a=$

• B

  $b=$

$\frac{\mathrm{4x}}{1-6\text{ix}}-\frac{\mathrm{2i}}{3-i}$

• A

  $a=$

• B

  $b=$

If $2x+3xi+2y=28+9i$ , what are $x$ and $y$ ?

Make up a quadratic equation (using all real numbers) that has two non-real roots, and solve it.

• A

  Find the two complex numbers (of course in the form $z=a+bi)$ that fill the condition $z^2=\mathrm{–2}i$ .

• B

  Check one of your answers to part (a), by squaring it to make sure you get $\mathrm{–2}i$ .