Expressing a complex number in simplest a + bi form is one of the most important concepts in algebra. A complex number is a number that consists of a real part, a and an imaginary part, bi. Expressing this number in a + bi form requires understanding of mathematical operations such as addition, subtraction, multiplication and division.
What is a Complex Number?
A complex number is a number composed of two parts: the real part, a, and the imaginary part, bi. The real part is a number that can be positive or negative. The imaginary part is a number that cannot be negative and is usually denoted with the letter i. An example of a complex number is 3 + 5i.
How to Express a Complex Number in a + bi Form?
The first step in expressing a complex number in a + bi form is to identify the real and imaginary parts of the number. To do this, one must look at the signs of the coefficients in the number. If the coefficient is positive, then it is the real part; if the coefficient is negative, then it is the imaginary part. Once the real and imaginary parts are identified, the number can be expressed in a + bi form.
Operations with Complex Numbers
Once a complex number is expressed in a + bi form, mathematical operations such as addition, subtraction, multiplication and division can be performed on it. To perform these operations, one must first identify the real and imaginary parts of the numbers, then perform the operations on the real parts and imaginary parts separately. For example, to add two complex numbers, 3 + 5i and 2 + 7i, one must first add the real parts (3 + 2 = 5) and add the imaginary parts (5i + 7i = 12i). The result is 5 + 12i.
Simplifying the Result
After performing an operation with complex numbers, it is important to simplify the result. This can be done by factoring out the imaginary part. For example, the result of the addition in the previous example is 5 + 12i. To simplify this, one must factor out the imaginary part, so that the result is 5 + 4i. The result is much simpler and easier to work with.
Expressing a complex number in simplest a + bi form is an important concept in algebra. It requires understanding of mathematical operations such as addition, subtraction, multiplication and division. After performing an operation with complex numbers, it is important to simplify the result by factoring out the imaginary part. With practice, expressing a complex number in a + bi form can become second nature.
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