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

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:** \[ 50 \]