Q. (−3+71i)+(9)=Express your answer in the form (a+bi).
Identify numbers to be added: Identify the numbers to be added.We have two numbers: a complex number (−3+71i) and a real number 9. The real number can be thought of as a complex number with an imaginary part of 0, so it is 9+0i.
Add real parts of complex numbers: Add the real parts of the complex numbers.The real part of (−3+71i) is −3, and the real part of 9+0i is 9. Adding these together gives us −3+9.
Perform addition of real parts: Perform the addition of the real parts.Calculating −3+9 gives us 6.
Add imaginary parts of complex numbers: Add the imaginary parts of the complex numbers.The imaginary part of (−3+71i) is 71i, and the imaginary part of 9+0i is 0i. Adding these together gives us 71i+0i.
Perform addition of imaginary parts: Perform the addition of the imaginary parts.Calculating 71i+0i gives us 71i.
Combine real and imaginary parts: Combine the results of the real and imaginary parts.We combine the real part 6 and the imaginary part 71i to express the sum in the form (a+bi).
Write final answer: Write the final answer.The sum of (−3+71i) and 9 is 6+71i.