Complex numbers are numbers that are expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of -1.
To simplify complex numbers, you need to combine like terms. This means adding or subtracting the real parts and adding or subtracting the imaginary parts. For example, to simplify (3 + 2i) + (4 - 5i), you would combine the real parts (3 + 4 = 7) and the imaginary parts (2i - 5i = -3i), giving you a simplified form of 7 - 3i.
Yes, you can simplify a complex number with a negative square root. The key is to rewrite the square root as i and then combine like terms as usual. For example, to simplify 3 + 2√-1, you would rewrite √-1 as i, giving you 3 + 2i.
Simplifying complex numbers involves combining like terms to get a more simplified form, while evaluating complex numbers involves finding the numerical value of a complex expression. For example, simplifying (3 + 2i) + (4 - 5i) would give you 7 - 3i, while evaluating this expression at x = 2 would give you 11 - 3i.
Yes, you can simplify an expression with multiple complex numbers by combining like terms, just as you would with a single complex number. For example, to simplify (3 + 2i) + (-4 + 5i) + (2 - i), you would combine the real parts (3 - 4 + 2 = 1) and the imaginary parts (2i + 5i - i = 6i), giving you a simplified form of 1 + 6i.