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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 8.171 (page 841)

Divide: $\frac{2 + 5 i}{5 - 2 i}$

Short Answer

Expert verified

The simplified form can be given as $i$

Step by step solution

01

Given information

We are given an equation $\frac{2 + 5 i}{5 - 2 i}$

02

Multiply the numerator and denominator by the complex conjugate of the denominator the complex conjugate of a+ib is a-ib

We get, $\frac{2 + 5 i}{5 - 2 i} 脳 \frac{5 + 2 i}{5 + 2 i}$

03

Simplify and write results in simple form

Hence we have

$\frac{10 + 4 i + 25 i + 10 i^{2}}{25 - 4 i^{2}} \frac{10 + 29 i - 10}{25 - (- 4)} \frac{29 i}{29} i$

04

Conclusion

The solution of the above equation is $i$

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Most popular questions from this chapter

In the following exercises, solve.

$\sqrt{2 n - 1} - 3 = 0$

Explain the difference of finding the $n^{t h}$ root of a number when the index is even compared to when the index is odd.

In the following exercise, write as a radical expression.

鈸� x^{\frac{1}{2}} 鈸� y^{\frac{1}{3}} 鈸� z^{\frac{1}{4}}

Use the Quotient Property to simplify square roots.

(a) $\sqrt{\frac{75 r^{6} s^{8}}{48 r s^{4}}}$

(b) $\sqrt[3]{\frac{24 x^{8} y 4}{81 x^{2} y}}$

(c) $\sqrt[4]{\frac{32 m^{9} n^{2}}{162 m n^{2}}}$

Simplify::
(a) $100^{\frac{1}{2}}$

(b) $27^{\frac{1}{3}}$

(c) $81^{\frac{1}{4}}$

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