The expressions that are equivalent to the given expression
(-√9 + √-4) - (2√576 + √-64) are
- -3 + 2i - 2(24) - 8i, and
What are Complex Numbers?
The sum of a real and an imaginary number is a complex number. A complex number is denoted by the letter z and has the form a + ib. Both a and b are real numbers in this case. The value 'a' is known as the real component and is indicated by Re(z), whereas 'b' is known as the imaginary part and is denoted by Im (z). ib is also known as an imaginary number.
What is 'i' in a complex number?
The letter 'i', often known as the iota, is used to denote the imaginary component of a complex integer. Additionally, the iota(i) may be used to find the square root of negative values. We know that i² = -1, therefore we utilize that to calculate the value of √-4 = √i²4 = ±2i. The essential characteristic of a complex number is the value of i² = -1.
How do we solve the given question?
We are asked to choose the expressions from the table equivalent to the given expression: (-√9 + √-4) - (2√576 + √-64).
To check for the equivalent expression, we simplify the given expression and check at each step if we get an expression from the given table.
(-√9 + √-4) - (2√576 + √-64)
= (-√3² + √(2i)²) - (2√24² + √(8i)²)
= (-3 + 2i) - (2(24) + 8i) ... (∵ √a² = a)
= -3 + 2i - 2(24) - 8i (Equivalent to one expression)
= -3 + 2i - 48 - 8i
= -51 - 6i (Equivalent to one expression)
∴ The expressions that are equivalent to the given expression
(-√9 + √-4) - (2√576 + √-64) are
- -3 + 2i - 2(24) - 8i, and
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