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  #### Resources tagged with Complex numbers similar to Polar Flower:
  
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  ### Conjugate Tracker
  
  ##### Stage: 5 Challenge Level:
  
  Make a conjecture about the curved track taken by the complex roots of a quadratic equation and use complex conjugates to prove your conjecture.
  
  ### Complex Sine
  
  ##### Stage: 5 Challenge Level:
  
  Solve the equation sin z = 2 for complex z. You only need the formula you are given for sin z in terms of the exponential function, and to solve a quadratic equation and use the logarithmic function.
  
  ### Roots and Coefficients
  
  ##### Stage: 5 Challenge Level:
  
  If xyz = 1 and x+y+z =1/x + 1/y + 1/z show that at least one of these numbers must be 1. Now for the complexity! When are the other numbers real and when are they complex?
  
  ### Complex Partial Fractions
  
  ##### Stage: 5 Challenge Level:
  
  To break down an algebraic fraction into partial fractions in which all the denominators are linear and all the numerators are constants you sometimes need complex numbers.
  
  ### Thebault's Theorem
  
  ##### Stage: 5 Challenge Level:
  
  Take any parallelogram and draw squares on the sides of the parallelogram. What can you prove about the quadrilateral formed by joining the centres of these squares?
  
  ### An Introduction to Complex Numbers
  
  ##### Stage: 5
  
  A short introduction to complex numbers written primarily for students aged 14 to 19.
  
  ### Thousand Words
  
  ##### Stage: 5 Challenge Level:
  
  Here the diagram says it all. Can you find the diagram?
  
  ### What Are Complex Numbers?
  
  ##### Stage: 5
  
  This article introduces complex numbers, brings together into one bigger 'picture' some closely related elementary ideas like vectors and the exponential and trigonometric functions and. . . .
  
  ### What Are Numbers?
  
  ##### Stage: 2, 3, 4 and 5
  
  Ranging from kindergarten mathematics to the fringe of research this informal article paints the big picture of number in a non technical way suitable for primary teachers and older students.
  
  ### Cube Roots
  
  ##### Stage: 5 Challenge Level:
  
  Evaluate without a calculator: (5 sqrt2 + 7)^{1/3} - (5 sqrt2 - 7)^1/3}.
  
  ### Target Six
  
  ##### Stage: 5 Challenge Level:
  
  Show that x = 1 is a solution of the equation x^(3/2) - 8x^(-3/2) = 7 and find all other solutions.
  
  ### Complex Countdown
  
  ##### Stage: 5 Challenge Level:
  
  Play a more cerebral countdown using complex numbers.
  
  ### Interactive Workout - Further
  
  ##### Stage: 5 Challenge Level:
  
  Give your further pure mathematics skills a workout with this interactive and reusable set of activities.
  
  ### Impedance Can Be Complex!
  
  ##### Stage: 5 Challenge Level:
  
  Put your complex numbers and calculus to the test with this impedance calculation.
  
  ### Sheep in Wolf's Clothing
  
  ##### Stage: 5 Challenge Level:
  
  Can you work out what simple structures have been dressed up in these advanced mathematical representations?
  
  ### Sextet
  
  ##### Stage: 5 Challenge Level:
  
  Investigate x to the power n plus 1 over x to the power n when x plus 1 over x equals 1.
  
  ### Three by One
  
  ##### Stage: 5 Challenge Level:
  
  There are many different methods to solve this geometrical problem - how many can you find?
  
  ### Napoleon's Theorem
  
  ##### Stage: 4 and 5 Challenge Level:
  
  Triangle ABC has equilateral triangles drawn on its edges. Points P, Q and R are the centres of the equilateral triangles. What can you prove about the triangle PQR?
  
  ### Complex Rotations
  
  ##### Stage: 5 Challenge Level:
  
  Choose some complex numbers and mark them by points on a graph. Multiply your numbers by i once, twice, three times, four times, ..., n times? What happens?
  
  ### 8 Methods for Three by One
  
  ##### Stage: 4 and 5 Challenge Level:
  
  This problem in geometry has been solved in no less than EIGHT ways by a pair of students. How would you solve it? How many of their solutions can you follow? How are they the same or different?. . . .
  
  ### Twizzle Twists
  
  ##### Stage: 4 Challenge Level:
  
  Make the twizzle twist on its spot and so work out the hidden link.
  
  ### Footprints
  
  ##### Stage: 5 Challenge Level:
  
  Make a footprint pattern using only reflections.
  
  ### Twizzle Wind Up
  
  ##### Stage: 4 Challenge Level:
  
  A loopy exploration of z^2+1=0 (z squared plus one) with an eye on winding numbers. Try not to get dizzy!
  
  ### Two and Four Dimensional Numbers
  
  ##### Stage: 5 Challenge Level:
  
  Investigate matrix models for complex numbers and quaternions.
  
  ### Twizzles Venture Forth
  
  ##### Stage: 4 Challenge Level:
  
  Where we follow twizzles to places that no number has been before.
  
  ### Pumping the Power
  
  ##### Stage: 5 Challenge Level:
  
  What is an AC voltage? How much power does an AC power source supply?