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soldier1979 [14.2K]
3 years ago
8

Which of the following statements about imaginary numbers are true? The square root of -1 is an imaginary number. is an imaginar

y number. i is an imaginary number. If an imaginary number is combined with a real number, the result is a complex number. Imaginary numbers aren’t practical
Mathematics
2 answers:
AveGali [126]3 years ago
7 0
All of those statements are true about imaginary numbers

Dmitry_Shevchenko [17]3 years ago
3 0

Answer:

The square root of -1 is an imaginary number: TRUE.

<em>i</em> is an imaginary number: TRUE.

If an imaginary number is combined with a real number, the result is a <em>complex number</em>: TRUE.

Imaginary numbers aren't practical: FALSE.

Step-by-step explanation:

<h3>First Part: \\ i = \sqrt{-1}</h3>

Imaginary numbers were the result of finding solutions for equations that require taking the square roots of negative numbers:

\\ \sqrt{-36} = \sqrt{-1*36} =\sqrt{-1} * \sqrt{36} = \sqrt{-1} *6 = 6i.

<em>Thus, the square root of -1 is an imaginary number</em>, and so \\ i since they are, in fact, the same: \\ i = \sqrt{-1}, which represents the <em>imaginary unit</em>. A consequence of that is \\ i^{2} = -1.

<h3>Second Part: a complex number is the result of combining an imaginary number with a real number.</h3>

A <em>complex number </em>is a quantity having <em>both a real and an imaginary part, </em>and are of the form<em> </em>\\ a + ib, since <em>imaginary numbers</em> <em>cannot</em> be represented on the <em>axis of real numbers</em>. They actually have their own axis called <em>imaginary axis</em>.

Both axes, then, form what is known as <em>complex plane</em> or <em>Argand diagram</em>, where <em>complex numbers</em> are represented.

In fact, a complex number with no real part is a <em>pure imaginary number</em>, and, conversely, a complex number with no imaginary number is a <em>pure real number</em>.  

<h3>Third Part: imaginary numbers are practical</h3>

Historically, Heaviside (1850-1925) "adapted complex numbers to the study of electrical circuits" [Wikipedia, 2019].

As a result, imaginary numbers are use to solve problems regarding electrical alternating current theory in <em>Electrical Engineering</em>, and they are represented by \\ j instead of \\ i, since \\ i is the symbol for electrical current.

There are many other applications on Quantum Mechanics, Dynamic Equations, signals analysis, control theory, fractal geometry, and so on.

Thus, imaginary numbers are use <em>in practice</em> to solve many problems in Science, Engineering, and Mathematics.

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