Answered

Discover a wealth of knowledge at Westonci.ca, where experts provide answers to your most pressing questions. Get quick and reliable solutions to your questions from a community of experienced experts on our platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

4

Ramon was asked to write the quotient 3 - i

in the

a + bi form. He began this way:

(3-i)

(3-i)

4(3-i)

(3² + (²)

112 - 41)

9 - 1

(12 - 4i)

8

11

(3-i)

2

Find Ramon's error and correct it (algebraically or in

words) so that he arrives at the accurate final solution.

Sagot :

MrRoyal

Answer:

[tex]\frac{4}{3 - i} = \frac{6}{5} + \frac{2}{5}i[/tex]

Step-by-step explanation:

Given

[tex]\frac{4}{3 - i}[/tex]

See attachment for question

Required

Correct Ramon's error

Start by rationalizing the expression:

[tex]\frac{4}{3 - i} = \frac{4}{3 - i}*\frac{3 + i}{3 + i}[/tex]

[tex]\frac{4}{3 - i} = \frac{4(3 + i)}{(3 - i)(3 + i)}[/tex]

Expand

[tex]\frac{4}{3 - i} = \frac{12 + 4i}{3^2 - i^2}[/tex]

[tex]\frac{4}{3 - i} = \frac{12 + 4i}{9 - i^2}[/tex]

In complex numbers:

[tex]i^2 = -1[/tex]

So:

[tex]\frac{4}{3 - i} = \frac{12 + 4i}{9 - (-1)}[/tex]

[tex]\frac{4}{3 - i} = \frac{12 + 4i}{9 +1}[/tex]

[tex]\frac{4}{3 - i} = \frac{12 + 4i}{10}[/tex]

Split fraction

[tex]\frac{4}{3 - i} = \frac{12}{10} + \frac{4i}{10}[/tex]

[tex]\frac{4}{3 - i} = \frac{6}{5} + \frac{2}{5}i[/tex]

View image MrRoyal
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.