Use the complex conjugate to find the absolute value of 8 + 12i

Solution:

Given complex number 8 + 12i

We know that the complex conjugate of 8 + 12i is 8 - 12i

The absolute value of a complex number can be calculated as the product of it with its complex conjugate

(8 + 12i)(8 - 12i) = 8(8) +8(-12i) +12i(8) + 12i(-12i)

(8 + 12i)(8 - 12i) = 64 - 96i + 96i - 144(i²)

(8 + 12i)(8 - 12i) = 64 - 144(-1)

(8 + 12i)(8 - 12i) = 64 + 144

(8 + 12i)(8 - 12i) = 208

Therefore, the absolute value is 208

Use the complex conjugate to find the absolute value of 8 + 12i

Summary:

Using the complex conjugate to find the absolute value of 8 + 12i, we get 208.