Chapter 1- Complex Numbers

Question 1

What is a complex number?

Answer 1

The sum of real and imaginary numbers, eg 3 + 2i

Question 2

What form is a complex number written in?

Answer 2

z=a+bi
Re (z) = a
Im (z) = b

Question 3

What is the pattern for i to the power of something?

Answer 3

Even indices: -1 or 1
Odd indices: -i or i

Question 4

What is the complex conjugate of z= a + bi

Answer 4

z*= a-bi
Together they are the complex conjugate pair (if one is a root, the other is also a root)

Question 5

What are some common tricks used in complex number questions?

Answer 5

-Equating the real and imaginary parts of complex numbers (often give sim equations from one line)
-Using the discriminant
-To find a quadratic, multiply using (z-(x+yi)) and (z-(x-yi))