If `(a + i b) (c + i d) (e + if) (g + i h) = A + i B`, then show that `(a^2+b^2)(c^2+d^2)(e^2+f^2)(g^2+h^2)=A^2+B^2`

Explanation

To solve the problem, we need to show that if \((a + ib)(c + id)(e + if)(g + ih) = A + iB\), then \((a^2 + b^2)(c^2 + d^2)(e^2 + f^2)(g^2 + h^2) = A^2 + B^2\).

### Step-by-step Solution:

1. **Define the Complex Numbers**:
Let \( Z_1 = a + ib \), \( Z_2 = c + id \), \( Z_3 = e + if \), and \( Z_4 = g + ih \).
Thus, we have:
\[
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