Questions: Evaluate the expression (3+2 i)+(8-5 i) and write the result in the form a+bi.

Transcript text: Evaluate the expression $(3+2 i)+(8-5 i)$ and write the result in the form $a+b i$.

Solution

Solution Steps

To evaluate the expression $(3+2i) + (8-5i)$, we need to add the real parts and the imaginary parts separately. The real parts are $3$ and $8$, and the imaginary parts are $2i$ and $-5i$. The result will be in the form $a + bi$.

Step 1: Identify the Complex Numbers

We start with the complex numbers given in the expression: \[ z_1 = 3 + 2i \quad \text{and} \quad z_2 = 8 - 5i \]

Step 2: Add the Real and Imaginary Parts

To find the sum $z_1 + z_2$, we add the real parts and the imaginary parts separately: \[ \text{Real part: } 3 + 8 = 11 \] \[ \text{Imaginary part: } 2 + (-5) = -3 \]

Step 3: Write the Result in Standard Form

Combining the results from the previous step, we express the sum in the form $a + bi$: \[ z_1 + z_2 = 11 - 3i \]