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

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 $a+b i$.
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Solution

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Solution Steps

To evaluate the expression (3+2i)+(85i)(3+2i) + (8-5i), we need to add the real parts and the imaginary parts separately. The real parts are 33 and 88, and the imaginary parts are 2i2i and 5i-5i. The result will be in the form a+bia + bi.

Step 1: Identify the Complex Numbers

We start with the complex numbers given in the expression: z1=3+2iandz2=85i z_1 = 3 + 2i \quad \text{and} \quad z_2 = 8 - 5i

Step 2: Add the Real and Imaginary Parts

To find the sum z1+z2z_1 + z_2, we add the real parts and the imaginary parts separately: Real part: 3+8=11 \text{Real part: } 3 + 8 = 11 Imaginary part: 2+(5)=3 \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+bia + bi: z1+z2=113i z_1 + z_2 = 11 - 3i

Final Answer

The result of the expression (3+2i)+(85i)(3 + 2i) + (8 - 5i) is 113i \boxed{11 - 3i}

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