Complex Numbers — Quiz 4

Questions in this quiz (6)

1. What is $$\left(\sqrt{-48} - \sqrt{-27}\right)^2$$?

   • $$-1$$
   • $$-3$$
   • $$-1$$
   • $$3$$

2. The absolute value of a complex number $$a+bi$$, where $$a$$ and $$b$$ are real numbers and $$i^2=-1$$, is defined by $$\sqrt{a^2+b^2}$$. Which of the following has the smallest absolute value?

   • $$4i$$
   • $$-2+2i$$
   • $$3+3i$$
   • $$-1-i$$

3. Which of the following complex numbers is equal to $$\sqrt{-18}-\sqrt{-8}$$?

   • $$i\sqrt{2}$$
   • $$i\sqrt{26}$$
   • $$i\sqrt{10}$$
   • $$3i\sqrt{2}$$

4. Which of the following is equivalent to the given expression?$$(7+2i)(5-3i)-\sqrt{9i\times6i}$$

   • $$41-10i$$
   • $$41-i(11+3\sqrt{6})$$
   • $$35-21i$$
   • $$41+10i$$

5. If $$z = 2 + 3i$$, what is $$|z|^2$$?

   • $$13$$
   • $$4 + 9i$$
   • $$4 - 9i$$
   • $$9i$$

6. If $$z = 1 + i$$, what is the value of $$z^3$$?

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