maybe fix summary tag usage
This commit is contained in:
parent
32199c7b2c
commit
1321fdadc8
@ -40,8 +40,13 @@ $$\bar{z} = z -iy$$
|
||||
|
||||
- Multiply numerator and denominator by the conjugate of the denominator
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
||||
#### Example
|
||||
|
||||
</summary>
|
||||
|
||||
> \begin{align*}
|
||||
z_1 &= 5 + i \\
|
||||
z_2 &= 1 -i \\
|
||||
@ -51,6 +56,8 @@ $$\bar{z} = z -iy$$
|
||||
&= \frac{4 + 6i}{2} = 2 + 3i
|
||||
> \end{align*}
|
||||
|
||||
</details>
|
||||
|
||||
### Algebra and Conjugation
|
||||
|
||||
When taking complex conjugate of an algebraic expresion, we can replace $i$ by $-i$ before or after
|
||||
@ -148,6 +155,7 @@ $$e^{i\theta} = \cos\theta + i\sin\theta$$
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
||||
### Example 1
|
||||
|
||||
Write $z = -1 + i$ in exponential form
|
||||
@ -163,6 +171,7 @@ Write $z = -1 + i$ in exponential form
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
||||
### Example 2
|
||||
|
||||
The equations for a mechanical vibration problem are found to have the following mathematical
|
||||
@ -257,6 +266,7 @@ r^n(\cos\theta +i\sin\theta)^n &= r^n(\cos{n\theta} + i\sin{n\theta}) \\
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
||||
### Example 1
|
||||
|
||||
Write $1+i$ in polar form and use de Moivre's theorem to calculate $(1+i)^{15}$.
|
||||
@ -278,6 +288,7 @@ Write $1+i$ in polar form and use de Moivre's theorem to calculate $(1+i)^{15}$.
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
||||
### Example 2
|
||||
|
||||
Use de Moivre's theorem to show that
|
||||
@ -302,6 +313,7 @@ Use de Moivre's theorem to show that
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
||||
### Example 3
|
||||
|
||||
Given that $n \in \mathbb{N}$ and $\omega = -1 + i$, show that
|
||||
@ -325,6 +337,7 @@ $w^n + \bar{w}^n = 2^{\frac n 2 + 1}\cos{\frac{3n\pi} 4}$ with Euler's formula.
|
||||
|
||||
<details>
|
||||
<summary>
|
||||
|
||||
### Example
|
||||
|
||||
Find which complex numbers $z$ satisfy
|
||||
|
Loading…
Reference in New Issue
Block a user