In Exercises 37–52, perform the indicated operations and write the result in standard form.(- 2 + √-4)^2

Complex numbers are numbers that have a real part and an imaginary part, expressed in the form a + bi, where 'a' is the real part and 'b' is the coefficient of the imaginary unit 'i', which is defined as the square root of -1. Understanding complex numbers is essential for performing operations involving square roots of negative numbers, as seen in this problem.

The standard form of a complex number is a + bi, where 'a' and 'b' are real numbers. When performing operations on complex numbers, it is important to express the final result in this form to clearly identify the real and imaginary components. This helps in further calculations and applications in various fields, including engineering and physics.

Exponentiation of complex numbers involves raising a complex number to a power, which can be done using the distributive property and the properties of exponents. In this case, squaring the complex number requires applying the formula (a + bi)² = a² + 2abi + (bi)², where (bi)² equals -b². This process is crucial for simplifying the expression and obtaining the result in standard form.