91Ó°ÊÓ

Complex numbers consist of a real part and an imaginary part. The imaginary part involves the imaginary unit, which is denoted by the letter \( i \). This unit arises from the property that \( i^2 = -1 \).
Imaginary numbers form when negative numbers sit under a square root, such as \( \sqrt{-1} \). This square root cannot be resolved within the realm of real numbers, hence emerges \( i \).
Imaginary units have vast applications. They're crucial in electrical engineering and control systems, where alternating currents rely on them.
In essence, while the imaginary unit \( i \) may sound mystical, it's just a mathematical tool that gives coherence to computations involving square roots of negative numbers.

When expressing complex numbers, we aim for clarity, which is where the standard form comes in handy. A complex number is conventionally expressed in the form \( a + bi \), where \( a \) and \( b \) are real numbers.
This form holds significance as:

• The \( a \) represents the real part of the complex number.
• The \( bi \) represents the imaginary part, with \( i \) being the imaginary unit.

Writing complex numbers in standard form facilitates easier manipulation, especially when performing operations like addition or subtraction.
Through standard form, calculations stay organized, enabling practitioners to clearly identify both the real and imaginary components.

Just like in algebra, combining like terms is essential when dealing with complex numbers. It ensures equations are simplified and in their purest form.
In our given problem, "like terms" refer to terms that are either entirely real or include the same imaginary unit.
When combining:

• All pure number terms (real numbers) are added or subtracted from other pure number terms.
• All terms with the imaginary unit \( i \) combine with each other.

This grouping maintains coherence in operations, producing results like our exercise's final form: \(-14 + 20i\).
Such simplification is pivotal in solving more complex operations involving various properties of complex numbers.