Simplify. Write answers in the form a+b i, where a and b are real numbers. (2+√(3 i))/(5-4 i)

Name: Problem 73, Chapter 3: Algebra and Trigonometry
Uploaded: 2020-07-11T07:20:59-08:00
Duration: 3 min 5 s
Channel: Ankit Gupta
Description: Simplify. Write answers in the form a+b i, where a and b are real numbers. (2+√(3 i))/(5-4 i)

step 1 Here we have given expression as 2 plus square with 3 aorta whole divided by 4 minus 5 aorta. So

Simplify. Write answers in the form a+b i, where a and b are...

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Key Concepts

Standard Form of Complex Numbers

Expressing a complex number in standard form means writing it as a + bi, where a is the real part and b is the imaginary coefficient. This form is essential for performing arithmetic operations, making comparisons, or simplifying expressions involving complex numbers.

Rationalizing Complex Denominators

When an expression involves a complex number in the denominator, the process of rationalization involves multiplying the numerator and the denominator by the complex conjugate of the denominator. This operation removes the imaginary component from the denominator, simplifying the overall expression and making it easier to express in standard form.

Complex Numbers

Complex numbers are numbers that consist of a real and an imaginary component, generally expressed in the form a + bi. They allow for the solution of equations that have no real solutions and provide a framework to handle two-dimensional mathematical problems.

Square Root of a Complex Number

Finding the square root of a complex number involves expressing the number in a form that allows for the application of algebraic or polar methods, such as using De Moivre's theorem. This process helps in rewriting radical expressions involving complex numbers into the standard a + bi form.

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