Ch. 5 - Complex Numbers, Polar Coordinates and Parametric Equations

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Blitzer 3rd Edition

Ch. 5 - Complex Numbers, Polar Coordinates and Parametric Equations

Problema 9

Capitolo 5, Problema 9

In Exercises 9–20, find each product and write the result in standard form. −3i(7i − 5)

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Recall that the imaginary unit $i$ has the property $i^2 = -1$.

Distribute $-3i$ across the terms inside the parentheses: $-3i \times 7i$ and $-3i \times (-5)$.

Calculate each product separately: $-3i \times 7i = -21i^2$ and $-3i \times (-5) = 15i$.

Substitute $i^2$ with $-1$ in the expression $-21i^2$ to get $-21 \times (-1)$.

Simplify the expression to combine the real and imaginary parts, resulting in a number in the form $a + bi$.

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Imaginary Unit (i)

The imaginary unit 'i' is defined as the square root of -1, with the property that i² = -1. It is fundamental in complex numbers and allows for the extension of the real number system to include solutions to equations like x² + 1 = 0.

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Percorso guidato

06:01

i & j Notation

Multiplication of Complex Numbers

Multiplying complex numbers involves using the distributive property (FOIL method) and applying the rule i² = -1. Each term is multiplied carefully, combining like terms and simplifying to express the result in standard form a + bi.

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Percorso guidato

5:02

Multiplying Complex Numbers

Standard Form of a Complex Number

The standard form of a complex number is written as a + bi, where 'a' is the real part and 'b' is the coefficient of the imaginary part. Expressing results in this form clearly separates real and imaginary components for easier interpretation.

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04:47

Complex Numbers In Polar Form

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