2. 5implify and write in the rectangular form 21) $$ 60 j^{8}+10 j^{4}-20 j^{20} $$

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To simplify the expression and write it in rectangular form, let's analyze each term involving the imaginary unit $$ j $$:

$$ 60j^{8} + 10j^{4} - 20j^{20} $$

Since $$ j $$ is the imaginary unit, it has the property that $$ j^4 = 1 $$. Therefore, any exponent of $$ j $$ can be reduced by taking it modulo 4.

1. **Simplify each term:**
   - $$ j^8 = (j^4)^2 = 1^2 = 1 $$
   - $$ j^4 = 1 $$
   - $$ j^{20} = (j^4)^5 = 1^5 = 1 $$

2. **Substitute the simplified values back into the expression:**
   $$
   60j^{8} + 10j^{4} - 20j^{20} = 60(1) + 10(1) - 20(1) = 60 + 10 - 20 = 50
   $$

3. **Express in rectangular form:**
   The result is a real number with no imaginary part, so the rectangular form is simply:
   $$
   50 + 0j
   $$
   However, it's common to present just the real part when the imaginary part is zero.

**Final Answer:**
$$ 50 $$
The simplified rectangular form of the expression is $$ 50 $$.

2. 5implify and write in the rectangular form 21) \( 60 j^{8}+10 j^{4}-20 j^{20} \)

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