Find the complex number z and write it in the form a+ bi if z=3+(2 i)/(2-i √(2))

Name: Problem 36, Chapter 10: Higher Level Mathematics
Uploaded: 2022-02-07T17:28:27-08:00
Duration: 2 min 40 s
Channel: Avinash Vishwakarma
Description: Find the complex number z and write it in the form a+ bi if z=3+(2 i)/(2-i √(2))

step 1 In this problem we have to find the complex number z that is 3 plus 2 i by minus i root where i

Find the complex number z and write it in the form a+ bi if...

Key Concepts

Arithmetic Operations with Complex Numbers

Operations such as addition, subtraction, multiplication, and division on complex numbers follow algebraic rules along with the special property i² = -1. Mastery of these operations is essential for manipulating expressions and solving equations involving complex numbers.

Rationalizing Denominators

Rationalizing the denominator in an expression with complex numbers involves eliminating the imaginary unit from the denominator. This is typically achieved by multiplying the numerator and denominator by the complex conjugate of the denominator, thereby converting the denominator into a real number.

Standard Form (a+bi)

Writing a complex number in standard form, a + bi, clearly separates the real part (a) from the imaginary part (b). This form is essential for performing arithmetic operations and for easily identifying the magnitude and argument in complex analysis.

Complex Numbers

Complex numbers are numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit with the property i² = -1. They extend the real number system and are used to solve equations that do not have real solutions.

Complex Conjugate

The complex conjugate of a complex number a + bi is a - bi. The conjugate is a crucial tool in complex arithmetic, particularly in rationalizing denominators, because multiplying a complex number by its conjugate yields a real number.

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