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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 8.172 (page 1069)

Divide: $\frac{1 + 6 i}{6 - i}$

Short Answer

Expert verified

The solution of the above equation is i

Step by step solution

01

Given information

We are given an equation $\frac{1 + 6 i}{6 - i}$

02

Multiply the numerator and denominator by the complex conjugate of the denominator. The complex conjugate of a+ibis a-ib

$\frac{1 + 6 i}{6 - i} \times \frac{6 + i}{6 + i}$

03

Simplify and write results in simple form

$\frac{6 + i + 36 i - 6}{36 - i^{2}} \frac{37 i}{37} i$

04

Conclusion

The solution of the above equation is $i$

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Most popular questions from this chapter

In the following exercises, factor each trinomial of the form

$x^{2} + b x + c x^{2} - 12 - 11 x$

Factor completely, $5 x^{3} + 15 x^{2} - 20 x$

In the following exercises, factor the greatest common factor from each polynomial.

$- 6 a^{3} b - 12 a^{2} b^{2} + 18 a b^{2}$

In the following exercises, simplify.

a. $\sqrt{48 b^{5}} - \sqrt{75 b^{5}}$

b. $8 \sqrt[3]{64 q^{6}} - 3 \sqrt[3]{125 q^{6}}$

In the following exercises, factor the greatest common factor from each polynomial.

$21 p q^{2} + 35 p^{2} q^{2} - 28 q^{3}$

See all solutions

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