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oksano4ka [1.4K]
3 years ago
8

Find the multiplicative inverse of 3 − 2i. Verify that your solution is corect by confirming that the product of

Mathematics
1 answer:
leonid [27]3 years ago
4 0

Answer:

\frac{3}{13} + \frac{2i}{13}

Step-by-step explanation:

The multiplicative inverse of a complex number y  is the complex number z such that (y)(z) = 1

So for this problem we need to find a number z such that

(3 - 2i) ( z ) = 1

If we take z = \frac{1}{3-2i}

We have that

(3- 2i)\frac{1}{3-2i} = 1 would be the multiplicative inverse of 3 - 2i

But remember that 2i = √-2 so we can rationalize the denominator of this complex number

\frac{1}{3-2i } (\frac{3+2i}{3+2i } )=\frac{3+2i}{9-(4i^{2} )} =\frac{3+2i}{9-4(-1)} =\frac{3+2i}{13}

Thus, the multiplicative inverse would be \frac{3}{13} + \frac{2i}{13}

The problem asks us to verify this by multiplying both numbers to see that the answer is 1:

Let's multiplicate this number by 3 - 2i to confirm:

(3-2i)(\frac{3+2i}{13}) = \frac{9-4i^{2} }{13}  =\frac{9-4(-1)}{13}= \frac{9+4}{13} = \frac{13}{13}= 1

Thus, the number we found is indeed the multiplicative inverse of  3 - 2i

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What is the multiplication problem that means the same thing as the division problem 1/9 divided by 12?
lianna [129]

<em>/Hello!</em>

<u><em>See below</em></u>

<em>We need to find x. X being the answer to 1/9 divided by 12.</em>

<em>1/9÷12=1/108. </em>

  • <em>=1×1/9×12</em>
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<em>Now that we know what "x" equals, we can divide the others.</em>

<em>1/9x12=1 and  3/9 ------simplifed is------1 and 1/3</em>

<em>Convert any mixed numbers to fractions</em>

<em>.</em>

<em>Then your initial equation becomes:</em>

<em>1/9×12/1</em>

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<em>=1×12/9×1</em>

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Therefore, your answer is B. 1/9 x 1/12

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