\( 1.1 .2 \frac { ( 3 c i s 23 ^ { \circ } ) ( 4 c i s 7 ^ { \circ } ) } { ( c i s 15 ^ { \circ } ) ( 6 c i s 5 ^ { \circ } ) } \)

To simplify the expression \[ 1.1 \cdot 2 \cdot \frac{(3 \text{cis} 23^\circ)(4 \text{cis} 7^\circ)}{(\text{cis} 15^\circ)(6 \text{cis} 5^\circ)} \] we will follow these steps: 1. **Multiply the constants and the cis terms in the numerator.** 2. **Multiply the constants and the cis terms in the denominator.** 3. **Divide the results from step 1 by the results from step 2.** 4. **Combine the results with the constant factor \(1.1 \cdot 2\).** ### Step 1: Multiply the constants and the cis terms in the numerator The numerator is: \[ (3 \text{cis} 23^\circ)(4 \text{cis} 7^\circ) = 3 \cdot 4 \cdot \text{cis}(23^\circ + 7^\circ) = 12 \text{cis}(30^\circ) \] ### Step 2: Multiply the constants and the cis terms in the denominator The denominator is: \[ (\text{cis} 15^\circ)(6 \text{cis} 5^\circ) = 6 \cdot \text{cis}(15^\circ + 5^\circ) = 6 \text{cis}(20^\circ) \] ### Step 3: Divide the results from step 1 by the results from step 2 Now we have: \[ \frac{12 \text{cis}(30^\circ)}{6 \text{cis}(20^\circ)} = \frac{12}{6} \cdot \text{cis}(30^\circ - 20^\circ) = 2 \text{cis}(10^\circ) \] ### Step 4: Combine the results with the constant factor \(1.1 \cdot 2\) Now we multiply by \(1.1 \cdot 2\): \[ 1.1 \cdot 2 \cdot 2 \text{cis}(10^\circ) = 2.2 \cdot 2 \text{cis}(10^\circ) = 4.4 \text{cis}(10^\circ) \] ### Final Result Thus, the simplified expression is: \[ 4.4 \text{cis}(10^\circ) \]