Operations with Complex Numbers

Simplifying Negative Radicals

100

Simplify: 

sqrt(-36)

What is 

6i

200

Simplify: 

sqrt(-32)

What is: 

4isqrt(2)

300

Simplify: 

3sqrt(-144)

What is: 

36i

400

Simplify: 

sqrt(-45+21)

What is: 

2isqrt(6)

500

Simplify: 

-4sqrt(-60-12)+sqrt(-18)

What is: 

-21isqrt(2)

Adding & Subtact Complex Numbers

100

Simplify:

(4i)+(2i)

What is:

6i

200

Simplify:

(4-4i)-(7+3i)

What is:

-3-7i

300

Simplify:

(3+9i)-(3+2i)

What is:

7i

400

Simplify:

-2(-3/4+4i)-(9-2i)

What is:

-15/2-6i

500

Simplify:

(-2+3i)/4+(4-3i)/2

What is:

3/2-(3i)/4

Powers of i

100

Simplify:

i^2

i^3

i^4

What is:

i^2=-1

i^3=-i

i^4=1

200

Simplify:

i^597

What is:

i

300

Simplify:

6i^14-17i^50

What is:

6*(i^4)^2*i^2-17*(i^4)^12*i^2

6*1*-1-17*1*-1

11

400

Simplify:

(i^3)^7*i^-13

What is:

i^21*i^-13=i^8=(i^4)^2

1

500

Simplify:

(5i^7+8i^16)/(10i^37)

What is:

(-5i^4i^3+8(i^4)^4)/(10(i^4)^9i)

(-5i+8)/(10i)*(-i)/(-i)

-1/2-(4i)/5

Multiplying Complex Numbers

100

Simplify:

(3i)(7i)

What is:

-21

200

Simplify:

3(-2+7i)

What is:

-6+21i

300

Simplify:

2i(5-4i)

What is:

8+10i

400

Simplify:

(3+i)(-5+3i)

What is:

-18+4i

500

Simplify:

(4+3isqrt(2))^2

What is:

-2+24isqrt(2)

Other Imaginary Things

100

You gain access to this kingdom through a rabbit hole, which might be on the banks of the Thames

What is Wonderland?

200

Meaning "old man of the desert", Shai-Halud is the term for the giant worms of Arrakis in this novel & film adaptation

What is Dune?

300

Seen here under the Fremont Bridge in Seattle is a depiction of one of these creatures

What is a troll?

400

Linguist Marc Okrand created this fictional language spoken by Worf (among others) on television

What is Klingon?

500

Thomas More created this island in 1516, from Greek for "no place"; based on rational thought & no poverty, is it beyond man's reach?

What is Utopia?