Problem 3 - College Algebra

Question

In Exercises \(1-8,\) add or subtract as indicated and write the result in standard form. $$(3+2 i)-(5-7 i)$$

Step-by-Step Solution

Answer

The result after subtracting the two complex numbers is \(-2 + 9i\).

Step 1: Identify the Real and Imaginary Parts

The first complex number is \(3+2i\), so its real part is 3 and its imaginary part is \(2i\). The second complex number is \(5-7i\), so its real part is 5 and its imaginary part is \(-7i\).

Step 2: Perform the Subtraction

Subtraction of complex numbers is done component-wise, meaning the real parts are subtracted from each other as are the imaginary parts. The result is: \((3+2i) - (5-7i) = (3-5) + (2i - (-7i)) = -2 + 9i\)

Step 3: Write the Result in Standard Form

In the standard form of a complex number, real and imaginary parts are written separately. Thus, the final result after subtraction will be \(-2 + 9i\) which is in the standard form.