Question 1

Question

Similarities and differences between $\mathbb{C}$ and ${\mathbb{R}}^2$.

Answer

Similarities

• Both have one $\mathbb{R}$ axis
• They can express ODEs (even though in different ways)

Differences

• Angles in ${\mathbb{R}}^2$ are usually expressed as $2\pi$, whereas $\mathbb{C}$ is in $\pi$
  • In $\mathbb{C}$ quadrants 1 and 2 are $\pi$; quadrants 3 and 4 are $-\pi$
• They cannot directly be translated to each other without losing data because imaginary numbers
• You can multiply pairs in ${\mathbb{R}}^2$ such as $(x_1,y_1)\times (x_2,y_2)=(x_1{x}_2,y_1{y}_2)$