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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. 8.174 (page 842)

Divide, writing the answer in standard form: $\frac{- 2}{- 1 + 2 i}$

Short Answer

Expert verified

The solution of the above equation is $\frac{2}{5} + \frac{4}{5} i$

Step by step solution

01

Given information

We are given an equation $\frac{- 2}{- 1 + 2 i}$

02

Multiply the numerator and denominator by thecomplex conjugate of the denominator.

$\frac{- 2}{- 1 + 2 i} 脳 \frac{- 1 - 2 i}{- 1 - 2 i}$

03

Multiply in the numerator and use the Product ofComplex Conjugates Pattern in the denominator.

$\frac{- 2 (- 1 - 2 i)}{1 - 4 i^{2}}$

04

Simplify

$\frac{2 + 4 i}{1 - 4 (- 1)} \frac{2 + 4 i}{1 + 4} \frac{2 + 4 i}{5}$

05

Write in standard form

We have, $\frac{2}{5} + \frac{4}{5} i$

06

Conclusion

The solution of the above equation is $\frac{2}{5} + \frac{4}{5} i$

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