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CLEP General Mathematics: Complex Numbers

Subjects : clep, math
Instructions:
  • Answer 50 questions in 15 minutes.
  • If you are not ready to take this test, you can study here.
  • Match each statement with the correct term.
  • Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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. Formula: z1 · z2 = (a + bi)(c + di) = ac +adi +cbi +bdi² = (ac - bd) + (ad +cb)i - when you multiply a complex number by its conjugate - you get a real number.






2. Root negative - has letter i






3. The field of all rational and irrational numbers.






4. What about dividing one complex number by another? Is the result another complex number? Let's ask the question in another way. If you are given four real numbers a -b -c and d - can you find two other real numbers x and y so that






5. Multiply moduli and add arguments






6. It is an amazing fact that by adjoining the imaginary unit i to the real numbers we obtain a complete number field called






7. R?¹(cos? - isin?)






8. 1. i^2 = -1 2. Every complex number has the 'Standard Form': a + bi for some real a and b. 3. For real a and b - a + bi = 0 if and only if a = b = 0 4. (a + bi) = (c + bi) = (a + c) + ( b + d)i 5. (a + bi)(c + bi) = ac + bci + adi + bdi^2 =(ac - bc






9. When two complex numbers are subtracted from one another.






10. y / r






11. We consider the a real number x to be the complex number x+ 0i and in this way we can think of the real numbers as a subset of






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






13. (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






14. Starts at 1 - does not include 0






15. When two complex numbers are multipiled together.






16. Rotates anticlockwise by p/2






17. A plot of complex numbers as points.






18. Have radical






19. 2ib






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






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






22. 3






23. 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






24. V(x² + y²) = |z|






25. (e^(iz) - e^(-iz)) / 2i






26. xpressions such as ``the complex number z'' - and ``the point z'' are now






27. Complex Plane = i - Use the distance formula to determine the point's distance from zero - or - the absolute value.






28. 2nd. Rule of Complex Arithmetic

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29. I^2 =






30. E^(i?) = cos? + isin? ; e^(ip) + 1 = 0

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






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






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

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34. To simplify the square root of a negative number






35. 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






36. V(zz*) = v(a² + b²)






37. Notice that rules 4 and 5 state that we complex numbers together - we can divide by c + di if c and d are not both zero. But there is a much easier way to do division.

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38. (2+i)(2i-3) you would use the foil methom which is first outter inner last. (2x2i)(2x-3)(ix2i^2)(ix(-3) =i-8






39. Not on the numberline






40. (2-3i)-(4+6i)you would distribute the negitive and combine your like terms and your answer is -2-9i






41. All the powers of i can be written as






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

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43. No i






44. A² + b² - real and non negative






45. The square root of -1.






46. 1






47. A + bi






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






49. When two complex numbers are divided.






50. 2a