To solve the complex number addition problem, we need to add the real parts and the imaginary parts separately. The real parts are 4 and 1, and the imaginary parts are 7i and -6i.
Step 1: Identify the Real and Imaginary Parts
To add the complex numbers (4+7i) and (1−6i), we first identify the real and imaginary parts of each number. The first complex number has a real part of 4 and an imaginary part of 7. The second complex number has a real part of 1 and an imaginary part of -6.
Step 2: Add the Real Parts
Add the real parts of the complex numbers:
4+1=5
Step 3: Add the Imaginary Parts
Add the imaginary parts of the complex numbers:
7+(−6)=1