Question

Perform the indicated operation on the complex numbers. (1-21i)/(4+i)

Answer 1

To perform the indicated operation on complex numbers (1-21i)/(4+i), we need to rationalize the denominator and simplify the complex fraction.

Step-by-step explanation:

To perform the indicated operation on complex numbers (1-21i)/(4+i), we need to rationalize the denominator.

Step 1: Multiply the numerator and denominator by the conjugate of the denominator.

• The conjugate of 4+i is 4-i.

Step 2: Perform the multiplication.

• Numerator: (1-21i)(4-i) = (4 + i - 84i + 21) = 25 - 83i
• Denominator: (4+i)(4-i) = (16 - i^2) = 16 + 1 = 17

Step 3: Simplify the complex fraction.

• (25 - 83i)/17

So, the result of the given operation is (25 - 83i)/17.