Find each sum or difference. Write answers in standard form. 3√7 - (4√7-i) -4i + (-2√7+5i)

Key Concepts

Radical Expressions

Radical expressions involve roots, such as square roots or cube roots. In this question, the term '√7' indicates a square root, which is a number that, when multiplied by itself, gives 7. Understanding how to manipulate these expressions, including addition and subtraction, is crucial for simplifying the overall expression.

Complex Numbers

Complex numbers are numbers that have a real part and an imaginary part, typically expressed in the form 'a + bi', where 'a' is the real part and 'bi' is the imaginary part. In this problem, terms like 'i' represent the imaginary unit, which is the square root of -1. Recognizing how to combine real and imaginary parts is essential for solving the expression.

Standard Form

Standard form for complex numbers is the format 'a + bi', where 'a' and 'b' are real numbers. When simplifying expressions involving complex numbers and radicals, it is important to express the final answer in this standard form. This ensures clarity and consistency in mathematical communication.