Simplify the expression to a, plus, b, i*a*+*bi* form:

square root of, 36, end square root, minus, square root of, minus, 4, end square root, minus, square root of, 121, end square root, plus, square root of, minus, 64, end square root

36​−−4​−121​+−64​

To simplify the given expression:

\[
\sqrt{36} - \sqrt{-4} - \sqrt{121} + \sqrt{-64}
\]

We'll handle each square root individually:

1. \(\sqrt{36} = 6\), because 6 is the positive square root of 36.
2. \(\sqrt{-4} = 2i\), because \(\sqrt{4} = 2\) and the square root of a negative number introduces the imaginary unit \(i\), so \(\sqrt{-4} = 2i\).
3. \(\sqrt{121} = 11\), because 11 is the positive square root of 121.
4. \(\sqrt{-64} = 8i\), because \(\sqrt{64} = 8\) and similarly, the negative sign introduces \(i\), so \(\sqrt{-64} = 8i\).

Now substitute these values back into the expression:

\[
6 - 2i - 11 + 8i
\]

Group the real and imaginary terms:

- Real part: \(6 - 11 = -5\)
- Imaginary part: \(-2i + 8i = 6i\)

Thus, the simplified expression in the form \(a + bi\) is:

\[
-5 + 6i
\]

Would you like further details on how I arrived at this? Here are some related questions you might find helpful:

1. What is the square root of a negative number in complex form?
2. How do you add and subtract complex numbers?
3. What are the properties of the imaginary unit \(i\)?
4. Can you explain why we group real and imaginary parts separately in complex numbers?
5. How does the magnitude of a complex number work?

**Tip:** Always remember that the square root of a negative number introduces the imaginary unit \(i\), where \(i^2 = -1\).

Simplify the expression to a + bi form: square root of 36, minus square root of minus 4, minus square root of 121, plus square root of minus 64

This step-by-step guide simplifies the expression √36 - √(-4) - √121 + √(-64) into the form a + bi. Explore key concepts in complex numbers, square roots, and imaginary units, suitable for students in Grades 9-11.

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