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:
z1=3+2iandz2=8−5i
Step 2: Add the Real and Imaginary Parts
To find the sum z1+z2, we add the real parts and the imaginary parts separately:
Real part: 3+8=11Imaginary 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:
z1+z2=11−3i
Final Answer
The result of the expression (3+2i)+(8−5i) is
11−3i