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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]
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