Here are the essential concepts you must grasp in order to answer the question correctly.
Imaginary Numbers
Imaginary numbers are defined as multiples of the imaginary unit 'i', where i is the square root of -1. They arise when taking the square root of negative numbers, which is not possible within the realm of real numbers. For example, √-16 can be expressed as 4i, since 4i * 4i = -16.
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Introduction to Complex Numbers
Standard Form of Complex Numbers
The standard form of a complex number is expressed as a + bi, where 'a' is the real part and 'b' is the imaginary part. In the context of the given question, after performing the indicated operations, the result should be simplified to this form to clearly represent the complex number. This helps in understanding the magnitude and direction of the number in the complex plane.
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Complex Numbers In Polar Form
Operations with Complex Numbers
Operations with complex numbers include addition, subtraction, multiplication, and division. When adding or subtracting complex numbers, you combine the real parts and the imaginary parts separately. For instance, when adding 5√-16 and 3√-81, you first convert them to their imaginary forms and then perform the addition, ensuring to keep the real and imaginary components distinct.
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