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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. 572 (page 856)

Multiply Complex Numbers
$(5 - \sqrt{- 12}) (- 3 + \sqrt{- 75})$

Short Answer

Expert verified

The Solution is $15 + 31 i \sqrt{3}$

Step by step solution

01

The Given Information

An expression is $(5 - \sqrt{- 12}) (- 3 + \sqrt{- 75})$

02

Simplify the terms to complex number

$= \sqrt{- 12} & \sqrt{- 75} = s i m p l f y i n g \sqrt{- 12} = i . \sqrt{12} = i . \sqrt{4} . \sqrt{3} = i . 2 . \sqrt{3} = 2 i \sqrt{3} = s i m p l f y i n g \sqrt{- 75} = i . \sqrt{75} = i . \sqrt{25} . \sqrt{3} = i . 5 . \sqrt{3} = 5 i \sqrt{3}$

03

Multiplying The terms

$= (5 - 2 i \sqrt{3}) (- 3 + 5 i \sqrt{3}) = - 15 + 25 i \sqrt{3} + 6 i \sqrt{3} - 30 i^{2} = - 15 + 31 i \sqrt{3} - 30 i^{2} = - 15 + 31 i \sqrt{3} + 30 = 15 + 31 i \sqrt{3}$

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