Answered

Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Discover precise answers to your questions from a wide range of experts on our user-friendly Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

The value of [tex]\((3 + 2i)^3\)[/tex] is:

A. [tex]\(62 + 9i\)[/tex]
B. [tex]\(46 - 9i\)[/tex]
C. [tex]\(46i - 9\)[/tex]
D. [tex]\(46i + 9\)[/tex]

Sagot :

GinnyAnswer
To solve for [tex]\((3 + 2i)^3\)[/tex], we will follow these steps:

1. Start by expressing the given complex number [tex]\(3 + 2i\)[/tex].

2. Apply the formula for raising a complex number to a power: [tex]\((a + bi)^3\)[/tex], where [tex]\(a = 3\)[/tex] and [tex]\(b = 2\)[/tex].

3. Raise the complex number [tex]\((3 + 2i)\)[/tex] to the power of three and compute the result in the form [tex]\(a + bi\)[/tex].

When you carry out the steps, the result is:

[tex]\[ (3 + 2i)^3 = -9 + 46i \][/tex]

So, the real part of [tex]\((3 + 2i)^3\)[/tex] is [tex]\(-9\)[/tex] and the imaginary part is [tex]\(46\)[/tex].

Therefore, the correct answer is:
(b) [tex]\(46i - 9\)[/tex]
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.