Question

Divide the following complex numbers and express the result (8+4i)/(3+i)

Answer 1

To divide the complex numbers (8+4i) and (3+i), multiply the numerator and denominator by the conjugate of the denominator, simplify, and express the result as a complex number.

Step-by-step explanation:

To divide the complex numbers (8+4i) and (3+i), we can use the concept of complex conjugates.

Multiply the numerator and denominator of the fraction by the conjugate of the denominator, which is (3-i).

The numerator becomes (8+4i)(3-i) = 24+8i-12i-4 = 20-4i.

The denominator becomes (3+i)(3-i) = 9-i² = 9+1 = 10.

Therefore, (8+4i)/(3+i) = (20-4i)/10 = 2-0.4i.