Operations with Complex Numbers

SIMPLIFY 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: 

8sqrt(-240)

What is: 

32isqrt(15)

500

Simplify:

sqrt(-45)+sqrt(-20)

What is:

5isqrt(5)

ADD & SUBTRACT

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:

(-3+4i)-(7-5i)-(-6+2i)

What is:

-4+7i

500

Simplify:

(sqrt(50)+sqrt(-45))-(sqrt(18)-sqrt(-80))

What is:

2sqrt(2)+7isqrt(5)

POWERS OF i

100

This is what each of the following simplify to:

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

MULTIPLICATION

100

Simplify:

2i(5-4i)

What is:

8+10i

200

Simplify:

(1+4i)(2+3i)

What is:

-10+11i

300

Simplify:

(-8+3i)^2

What is:

55-48i

400

Simplify:

(3+isqrt(2))(-5+3isqrt(2))

What is:

-21+4isqrt(2)

500

Simplify:

(4+3isqrt(20))(5-2isqrt(45))

What is:

200+6isqrt(5)

MORE IMAGINARY THINGS

100

You get to this imaginary place by falling down a rabbit hole, which might be on the banks of the Thames

What is Wonderland?

200

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

What is a troll?

300

You can burn around 400 cals. an hour, decrease stress & get in cardio doing this, throwing jabs & hooks at an imaginary foe

What is shadow boxing?

400

This imaginary line that circles the globe is also known as 0 degrees latitude

What is the equator?

500

The name of this imaginary island created by Sir Thomas More in 1576 is synonymous with a perfect place, and comes from the Greek for "nowhere"; pessimistic!

What is Utopia?