Evaluate the following:`\ x^4+4x^3+6x^2+4x+9,\ w h e n\ x=-1+isqrt(2)`

Explanation

To evaluate the expression \( x^4 + 4x^3 + 6x^2 + 4x + 9 \) when \( x = -1 + i\sqrt{2} \), we will follow these steps:

### Step 1: Calculate \( x^2 \)
Given \( x = -1 + i\sqrt{2} \),
\[ x^2 = (-1 + i\sqrt{2})^2 = (-1)^2 + 2(-1)(i\sqrt{2}) + (i\sqrt{2})^2 \]
Calculating each term:
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