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CLEP General Mathematics: Complex Numbers

Subjects : clep, math
Instructions:
  • Answer 50 questions in 15 minutes.
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  • Match each statement with the correct term.
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This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.
1. Derives z = a+bi






2. R?¹(cos? - isin?)






3. 2ib






4. I






5. All numbers






6. No i






7. We see in this way that the distance between two points z and w in the complex plane is






8. A complex number and its conjugate






9. V(zz*) = v(a² + b²)






10. (2i+3)/(9-i)for the denominator you multiply by the conjugate and what u do to the bottom u have to do to the top then you distribute the bottom then the top then add like terms then you simplify. 21i+25/17






11. All the powers of i can be written as






12. ½(e^(iz) + e^(-iz))






13. Has the opposite sign of a complex number; the conjugate of a + bi is a - bi






14. Cos n? + i sin n? (for all n integers)






15. (a + bi)(c + bi) =






16. A+bi






17. 4th. Rule of Complex Arithmetic






18. A² + b² - real and non negative






19. If z= a+bi is a complex number and a and b are real - we say that a is the real part of z and that b is the imaginary part of z






20. 2nd. Rule of Complex Arithmetic

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21. A subset within a field.






22. Like pi






23. The modulus of the complex number z= a + ib now can be interpreted as






24. The complex number z representing a+bi.






25. Any set of elements that satisfies the field axioms for both addition and multiplication and is a commutative division algebra.






26. A number that can be expressed as a fraction p/q where q is not equal to 0.






27. A + bi






28. The square root of -1.






29. Every complex number has the 'Standard Form':






30. For real a and b - a + bi =






31. Where the curvature of the graph changes






32. Not on the numberline






33. E ^ (z2 ln z1)






34. Multiply moduli and add arguments






35. 1st. Rule of Complex Arithmetic






36. 3






37. When you multiply two complex numbers a + bi and c + di FOIL the terms: (a + bi)(c + di) = (ac - bd) + (ad + bc)i






38. Ln(r e^(i?)) = ln r + i(? + 2pn) - for all integers n






39. The product of an imaginary number and its conjugate is






40. A + bi = z1 c + di = z2 - addition: z1 + z2 = (a + bi) + (c + di) = (a + c) + (b + d)i subtraction: z1 - z2 = (a - c) + (b - d)i






41. I^2 =






42. 1






43. 1






44. Starts at 1 - does not include 0






45. zn = (cos? + isin?)n = cosn? + isinn? - For all integers n

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46. I = imaginary unit - i² = -1 or i = v-1






47. To prove that number field every algebraic equation in z with complex coefficients has a solution we need

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48. When two complex numbers are divided.






49. A complex number may be taken to the power of another complex number.






50. (e^(-y) - e^(y)) / 2i = i sinh y







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