Powers of I

Complex Numbers and the powers of i

by Bette Horsington

​Complex Number

Multiple Choice

Simplify  $$\sqrt[]{-100}$$  

• 10
• -10
• 10i
• -10i

Multiple Choice

Simplify: $$\sqrt[]{-5}\left(\sqrt[]{-5}\right)$$  

• 5i
• -5i
• 5+i
• -5

Multiple Choice

What is the complex conjugate of  $$4-3i$$  ?

• A.  1/(4-3i)
• B. 1/(4+3i)
• C.  -4 + 3i
• D.  4 + 3i

Multiple Choice

Add and simplify: $$(5-2i)+(-7+8i)$$  

• -2+6i
• 12+6i
• -35-16i²
• -35 -16i

Multiple Choice

Multiply and simplify:  $$(3i)(-2+4i)$$  

• $$-6+12i$$  

• $$-12-6i$$  

• $$-2+7i$$  

• $$12+6i$$  

Multiple Choice

Multiply and simplify:  $$(4-3i)(-7-2i)$$  

• $$-23-29i$$  

• $$-34+13i$$  

• $$-34-29i$$  

Multiple Choice

Simplify $$\left(-6-2i\right)^2$$   (hint write it out twice!)

• 32
• 36-4i
• 36+24i
• 32+24i

Multiple Choice

$$\frac{5-8i}{3+2i}$$  , what do you do to divide?

• Multiply the top and bottom by 3-2i

• Multiply the top and bottom by 5 + 8i

• multiply the top by 5 + 8i and the bottom by 3 - 2i

• Multiply the top and bottom by -3 - 2i

Multiple Choice

Simplify  $$\frac{9}{6i}$$  

​Powers of i

Multiple Choice

Simplify: 

$$i^6$$  

• 1

• -1

• i

• -i

Multiple Choice

Simplify: 

$$i^{12}$$

• 1

• -1

• $$i$$  

• $$-i$$  

Multiple Choice

Simplify: 

$$i^9$$

• 1

• -1

• $$i$$  

• $$-i$$  

Multiple Choice

Simplify:

$$i^{15}$$

• 1

• -1

• $$i$$  

• $$-i$$  

Multiple Choice

Multiply $$4-3i$$  by its conjugate. 

• 7

• 25

• 16-9i

• 16+9i

Multiple Choice

Find the sum  $$(5-2i)+(-7+8i)$$  

• -2+6i
• 12+6i
• -35-16i²
• -35 -16i