Question

Find the difference of the following expression: open parentheses 3 plus i close parentheses minus left parenthesis 4 minus 5 i right parenthesis

Answer 1

The difference of the complex numbers (3 + i) and (4 - 5i) is calculated by changing the signs of the subtracted complex number, which gives the resulting complex number (-1 + 6i).

Step-by-step explanation:

To find the difference of the complex numbers (3 + i) and (4 - 5i), we perform a subtraction of the two expressions. First, apply the rule of subtraction by changing the signs of the second complex number and then adding accordingly: (3 + i) - (4 - 5i) becomes (3 + i) + (-4 + 5i).

Now, combine like terms - real numbers with real numbers and imaginary numbers with imaginary numbers:

• Real part: 3 + (-4) = -1
• Imaginary part: i + 5i = 6i

The resulting complex number is then (-1 + 6i).