1. Is it true that (If notgive the correct answer)

a)= i and i²= -1.

b) 3i is a complex number.

c) 5 + 2i is an imaginary number.

d) a + bi is the standard form of a complex number

2. Write in standard form of a complex numbera bi

a) 5b) 2ic)d)

3. Is it true that (if not explain why)Review Section R3

a)==*=i=i, wherea 0the restriction on square root

b)*==.( Note*=is true only fora 0, b 0)

c)*= i* i= i²*=-fora 0, b 0

4. Which solution is correct 4a or 4b?Explain your answer

Simplify:

4a)

4b)

5. Simplify

6.Is it true that (If notgive the correct answer)

a) i¹= Ib) i²= -1c) i³= -id) i⁴= 1

e) i²⁰= (i²)⁴= 1f) i²⁹= (i⁷)⁴*i¹= 1*i = Ig) i²⁴⁵= (i⁶²)⁴* i¹= i *(-1) = -i

7. Simplify: (See Section 1.3, Objective 3, Example 4. For more help see the "Frequently asked questions" on Blackboard, "Complex numbers. Powers of i")

a) i⁸b) i⁴⁵c) i¹²⁵

8. Is it true that (If not give the correct answer)

a) (a - b) (a + b) = a²- b²

b) (3 + i)(3 - i) = 3²- i²= 9 - 1 = 8

c) the factors (3 + i) and (3 - i) are called complex conjugates

d) multiply (2i + 5)(2i - 5)

9. a) Is it true that(a b)²= a²2ab + b²and we can use this formula to simplify our calculations

b) Simplify (2 -3i)²and (2 + 3i)²by applying the formula (a b)²= a²2ab + b²

10. Multiply using the corresponding formulas and write the answer in standard form a bi

a) -3i * ib) (i + 3)(i - 3)c) (2i -5)(2i + 5)d) (2 - 5i)²

11. a) Is it true that

a) a fraction containing a complex number in the denominator is in simplest form whenno imaginary number (no i)remains in thedenominator

b) this can be accomplished by multiplying the denominator of the form (a bi) by its complex conjugate. Of cause, this means that we must also multiply the numerator by the same quantity

c) to divideyou should multiply the numerator2and the denominatoribyiand apply the property

i²= -1

d) to divideyou should multiply the numeratoriand the denominator(2 -i)by(2 + i)and apply the formula(a - b) (a + b) = a²- b²

e) the standard form of a complex fractionis

f) Simplify===-=-=-

12) Divide and write the answer in standard form a bi

Remember:is the standard form for a complex fraction

a)b)c)