Questions: Simplify the expression to a+bi form: -√1-√(-128)-√121-√(-8)

Solution Steps

We start with the first term: \[ -\sqrt{1} = -1 \]

Next, we calculate the square root of \(-128\): \[ -\sqrt{-128} = -i\sqrt{128} = -i\sqrt{64 \cdot 2} = -i \cdot 8\sqrt{2} = -8\sqrt{2}i \]

Now, we compute the square root of \(121\): \[ -\sqrt{121} = -11 \]

Next, we find the square root of \(-8\): \[ -\sqrt{-8} = -i\sqrt{8} = -i\sqrt{4 \cdot 2} = -i \cdot 2\sqrt{2} = -2\sqrt{2}i \]

Now, we combine all the real parts and imaginary parts: Real part: \[ -1 - 11 = -12 \] Imaginary part: \[ -8\sqrt{2}i - 2\sqrt{2}i = -10\sqrt{2}i \]

Thus, the expression simplifies to: \[ -12 - 10\sqrt{2}i \]

This is the final result in the form \(a + bi\).

Final Answer