In Exercises 1–8, add or subtract as indicated and write the result in standard form. (7 + 2i) + (1 - 4i)
Table of contents
- 0. Review of Algebra4h 18m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations1h 43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 5m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 22m
- 10. Combinatorics & Probability1h 45m
- Appendix 1. Review of Real Numbers2h 24m
- Appendix 2. Linear Equations and Inequalities3h 42m
- OLD 9. Sequences, Induction, and Probability Coming soon
- 1. - OLD - Fundamental Concepts of Algebra Coming soon
- 2. - OLD - Equations and Inequalities Coming soon
- OLD 4. Rational Functions Coming soon
- OLD 2. Functions & Graphs Coming soon
- OLD 6. Exponential and Logarithmic Functions Coming soon
- OLD 7. Systems of Equations and Inequalities Coming soon
- OLD 8. Matrices and Determinants Coming soon
- OLD 9. Conic Sections Coming soon
1. Equations & Inequalities
The Imaginary Unit
Multiple Choice
Simplify the given square root. −75
A
25i3
B
5i3
C
3i5
D
75i
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Verified step by step guidance1
Identify the expression inside the square root: \(-75\).
Recognize that the square root of a negative number involves the imaginary unit \(i\), where \(i = \sqrt{-1}\).
Rewrite the expression as \(\sqrt{-75} = \sqrt{75} \cdot \sqrt{-1} = \sqrt{75} \cdot i\).
Simplify \(\sqrt{75}\) by factoring it into \(\sqrt{25 \times 3} = \sqrt{25} \cdot \sqrt{3}\).
Calculate \(\sqrt{25} = 5\), so the expression becomes \(5 \cdot \sqrt{3} \cdot i = 5i\sqrt{3}\).
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