Complex Numbers - Basic Skills

Powers of i and Simplifying Surds

100

Simplify the following: √(-36)

6i

200

What is i to the third power? Or i^3? 

-i

300

Simplify the following: √(-75)

5i√3

400

What is i⁷ ?

-i

500

Simplify the following: √(-200)

10i√2

600

√(-64)

8i

Adding & Subtracting Complex numbers

100

(7 +i)+(-4-2i)

3 - i

200

(9+2i) - (6+4i) 

3-2i

300

(-3+8i) + (-9+7i)

-12 + 15i

400

(5+4i) + (1+5i)

6 + 9i

500

(8 +i)-(-2-2i)

10+3i

600

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

-5 + 11i

Multiplying & Dividing Complex Numbers

100

(-8 -i)(1-5i)

-13 + 39i

200

(2i +2)(4i+2)

-4 + 12i

300

(-8+4i) / (4-8i)

(-64-48i) / 80 or (-4 - 3i) / 5

400

When (-3 - 2i) is multiplied by its conjugate, what is the result?

13

500

4(2+i) * (3-7i)

52-44i

600

(-4-2i) * (8-4i)

-24

Random

100

(4 +i)-(6+2i)

-2-i

200

What is a conjugate?

The opposite sign of the imaginary part of a complex number. Ex: (8-9i) -----> (8+9i)

300

i⁴ * i²

-1

400

(6 +2i)/(4+8i)

1/2 - 1/2 i

500

(3+5i)²

-16+30i

600

√(-3) * √(-3)

-3

Ms. Burke

100

What other subjects do I teach at leaving cert level?

Physics and Applied Maths

200

Where did I graduate university

NUIG

300

Am I a dog person or a cat person?

Dog 

400

How long have I been teaching at Clarin College

Since 2021 (This is my 3rd year)

500

Where did I teach before Clarin College?

Dublin

600

What is my favourite Maths topic?

Trigonometry

Powers of i

100

i² + i² 

-2

200

i² + i³

-1 + (-i) or (-1 - i)

300

3i² +4i⁴ + 5i⁸ +3

9

400

5i⁴ + 3i² +4i⁷ - 4 

-2 - 4i

500

-i (7i +8) -8(1+8i)

-1 -72i

600

i⁴*i*i⁸*i⁵

-1