Question

Find the product $(2+3 i)(-2-5 i)$.

   Find the product $(2+3 i)(-2-5 i)$.

Algebra & Trigonometry Problem Solver

Algebra & Trigonometry Problem Solver

Jerry R. Shipman,… 1st Edition

Chapter 31, Problem 19

Instant Answer

Solved by Expert Ankit Gupta

08/31/2020

Step 1

Step 1: Identify the two complex numbers to be multiplied: \( (2 + 3i) \) and \( (-2 - 5i) \). Show more…

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Find the product $(2+3 i)(-2-5 i)$.

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Key Concepts

Complex Numbers

Complex numbers are numbers written in the form a + bi, where 'a' is the real part and 'b' is the imaginary part. They extend the concept of one-dimensional number lines to a two-dimensional complex plane, enabling solutions to equations that do not have real solutions.

Imaginary Unit

The imaginary unit, denoted by i, is defined by the property that i² = -1. This key concept allows for the definition and manipulation of complex numbers, particularly when dealing with square roots of negative numbers.

Multiplication of Complex Numbers

Multiplying complex numbers involves applying the distributive property (or FOIL method) to each term, then combining like terms. This process requires careful handling of the imaginary unit, especially by replacing i² with -1 to simplify the resulting expression into the standard form a + bi.

Distributive Property

The distributive property is a fundamental algebraic rule used to multiply each term in one expression by every term in another. In the context of complex numbers, it enables the systematic expansion of the product before simplifying by combining like terms.

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