Find the following quotient. Write your answer in standard form for complex numbers. 2 + 4i2 − 4i

To find the quotient of the complex numbers (2 + 4i) / (2 - 4i), follow these steps:

Step 1: Multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of (2 - 4i) is (2 + 4i).

So, (2 + 4i) / (2 - 4i) * (2 + 4i) / (2 + 4i) = (2 + 4i) * (2 + 4i) / (2 - 4i) * (2 + 4i)

Step 2: Multiply out the numerator and the denominator.

Numerator: (2 + 4i) * (2 + 4i) = 4 + 16i + 16i^2 = 4 + 16i - 16 (since i^2 = -1) So, the numerator is -12 + 16i.

Denominator: (2 - 4i) * (2 + 4i) = 4 + 8i - 8i - 16i^2 = 4 - 16 (since i^2 = -1) So, the denominator is 20.

Step 3: Divide the real and imaginary parts of the numerator by the denominator.

So, (-12 + 16i) / 20 = -12/20 + 16i/20 = -0.6 + 0.8i

So, the quotient of (2 + 4i) / (2 - 4i) is -0.6 + 0.8i.