Homework 1.3

1.  Fill in the blanks.  The imaginary unit i is defined as i =​_______, where

=​_______.

2.  Decide whether the given statement is true or false. If​ false, correct the right side of the equation.

$\sqrt{–16}·\sqrt{–36}= –24$

Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

1. The given statement is false. The correct right side of the equation is _____   (Simplify your answer. Type your answer in the form a+bii. Type an exact​ answer, using radicals as​ needed.)
2. The given statement is true.

3. Decide whether the given statement is true or false. If​ false, correct the right side of the equation.

$i^{52}=–1$

Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

1. The given statement is false. The correct right side of the equation is _____  (Simplify your answer. Type your answer in the form a+bii.  Type an exact​ answer, using radicals as​ needed.)
2. The given statement is true.

4.   Identify the number as​ real, complex, pure​ imaginary, or nonreal complex.​ (More than one of these descriptions may​ apply.)

8.  Select all descriptions that may apply.

1. Pure imaginary
2. Nonreal complex
3. Complex
4. Real

5. Write the number as the product of a real number and i

$\sqrt{–108}$

6.  Write the number as the product of a real number and

$–\sqrt{–45}$

7.  Divide.

$\frac{\sqrt{–700}}{\sqrt{–100}}$

8.  Find the quotient.

$\frac{\sqrt{–84}}{\sqrt{12}}$

9. Divide.

$\frac{\sqrt{–24}}{\sqrt{–54}}$

10.  Write the number in standard form.

$\frac{–2+\sqrt{–8}}{2}$

11. Write the number in standard form.

$\frac{4–\sqrt{–72}}{2}$