Complex Numbers — Quiz 5

Questions in this quiz (8)

1. Assuming $$i^2 = -1$$, which of these complex numbers is $$(1 + 2i)^3$$ in simplified form?

   • $$-11 - 2i$$
   • $$-12 + 8i$$
   • $$-11 + 2i$$
   • $$12 - 8i$$

2. Assuming $$i^2 = -1$$, which of these complex numbers is equivalent to $$i^{6k+1} + i^{8k+3}$$, where $$k$$ is a positive integer?

   • $$i - 1$$
   • $$i$$
   • $$0$$
   • $$-i$$

3. Where $$i^2 = -1$$, which of these complex numbers is $$(2i^{45} + 5i^{44})^2$$ in simplified form?

   • $$2 + 5i$$
   • $$2i + 5$$
   • $$2i - 5$$
   • $$21 + 20i$$

4. Assuming $$i^2 = -1$$ and $$x$$ is real, what is the coefficient of the $$x$$-term of a third-degree polynomial with integer coefficients and solutions $$-\frac{3}{4}$$ and $$4i$$?

   • 64
   • 48
   • 3
   • 16

5. What is the distance in the complex plane between $$3 + 2i$$ and $$\left(3 + 2i\right)^2$$?

   • $$4\sqrt{26}$$
   • $$2\sqrt{10}$$
   • $$4\sqrt{10}$$
   • $$2\sqrt{26}$$

6. The graph of a complex number $$z$$ is in Quadrant II. Which of the following could be $$z$$?

   • $$-2 + 3i$$
   • $$3 + 2i$$
   • $$-1 - 2i$$
   • $$1 - 3i$$

7. Which of the following complex numbers is equivalent to rotating the point $$(1, 0)$$ by $$90^\circ$$ counterclockwise in the complex plane?

   • $$1+i$$
   • $$i$$
   • $$1-i$$
   • $$-1-i$$

8. Determine the value of$$x^2-2xy-y^2$$ if $$(x + yi)^2 = -4 + 5i^{95}$$

   • 1
   • -4
   • 9
   • -9