maybe fix summary tag usage

This commit is contained in:
Akbar Rahman 2021-10-14 15:33:38 +01:00
parent 32199c7b2c
commit 1321fdadc8
Signed by: alvierahman90
GPG Key ID: 20609519444A1269

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@ -40,8 +40,13 @@ $$\bar{z} = z -iy$$
- Multiply numerator and denominator by the conjugate of the denominator - Multiply numerator and denominator by the conjugate of the denominator
<details>
<summary>
#### Example #### Example
</summary>
> \begin{align*} > \begin{align*}
z_1 &= 5 + i \\ z_1 &= 5 + i \\
z_2 &= 1 -i \\ z_2 &= 1 -i \\
@ -51,6 +56,8 @@ $$\bar{z} = z -iy$$
&= \frac{4 + 6i}{2} = 2 + 3i &= \frac{4 + 6i}{2} = 2 + 3i
> \end{align*} > \end{align*}
</details>
### Algebra and Conjugation ### Algebra and Conjugation
When taking complex conjugate of an algebraic expresion, we can replace $i$ by $-i$ before or after 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> <details>
<summary> <summary>
### Example 1 ### Example 1
Write $z = -1 + i$ in exponential form Write $z = -1 + i$ in exponential form
@ -163,6 +171,7 @@ Write $z = -1 + i$ in exponential form
<details> <details>
<summary> <summary>
### Example 2 ### Example 2
The equations for a mechanical vibration problem are found to have the following mathematical 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> <details>
<summary> <summary>
### Example 1 ### Example 1
Write $1+i$ in polar form and use de Moivre's theorem to calculate $(1+i)^{15}$. 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> <details>
<summary> <summary>
### Example 2 ### Example 2
Use de Moivre's theorem to show that Use de Moivre's theorem to show that
@ -302,6 +313,7 @@ Use de Moivre's theorem to show that
<details> <details>
<summary> <summary>
### Example 3 ### Example 3
Given that $n \in \mathbb{N}$ and $\omega = -1 + i$, show that 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> <details>
<summary> <summary>
### Example ### Example
Find which complex numbers $z$ satisfy Find which complex numbers $z$ satisfy