Complex Number Games and Worksheets

Complex Number Games
Complex numbers might seem “imaginary,” but they are essential for everything from electrical engineering to quantum physics. These games transform abstract a + bi concepts into interactive challenges, helping students visualize the complex plane and master operations with ease.

Powers of i Game
The Goal: Simplify in for any integer n. Students learn to navigate the four-step cycle: i1 = i, i2 = -1, i3 = -i, and i4 = 1.
Key Concept: Recognizing the cyclic nature of powers of i.
Best for: Building the foundational speed needed for higher-level complex multiplication.
Play now: Powers of i Game

Plot Complex Numbers
The Goal: Correctly place complex numbers on the Argand plane. The game treats the Real part as the x-axis and the Imaginary part as the y-axis.
Key Concept: Visualizing a + bi as a coordinate (a, b).
Best for: Students transitioning from standard Cartesian coordinates to the complex plane.
Play now: Plot Complex Numbers

Quadratics with Complex Roots
The Goal: Solve quadratic equations where the discriminant (D = b2 - 4ac) is negative. Players learn to express solutions using i instead of simply saying “no real solution.”
Key Concept: Applying the quadratic formula to find conjugate pairs.
Best for: Moving beyond the limitations of real number algebra.
Play now: Complex Roots Challenge

Add & Subtract Complex Numbers
The Goal: Combine like terms by grouping real parts with real parts and imaginary parts with imaginary parts.
Key Concept: (a + bi) ± (c + di) = (a ± c) + (b ± d)i.
Best for: Reinforcing basic algebraic grouping rules within a new number system.
Play now: Add & Subtract Complex Numbers

Multiply Complex Numbers
The Goal: Use the FOIL method or distributive property to multiply two complex numbers, remembering to simplify i2 to -1.
Key Concept: Mastery of the identity i2 = -1 during expansion.
Best for: Preventing the common mistake of leaving i2 in the final answer.
Play now: Multiply Complex Numbers

Divide Complex Numbers
The Goal: Rationalize the denominator by multiplying the numerator and denominator by the complex conjugate.
Key Concept: Utilizing the conjugate (a - bi) to eliminate i from the denominator.
Best for: Mastering precision and multi-step algebraic manipulation.
Play now: Divide Complex Numbers

Magnitude & Modulus
The Goal: Calculate the “absolute value” or distance from the origin for a complex number using the Pythagorean theorem.
Key Concept:
Best for: Connecting complex numbers to geometry and trigonometry.
Play now: Magnitude of Complex Numbers

Distance between 2 Complex Numbers
The Goal: Find the distance between two points on the complex plane.
Key Concept: Applying the distance formula \(\sqrt{(a_2-a_1)^2 + (b_2-b_1)^2}\).
Best for: Understanding the spatial relationships between different complex values.
Play now: Distance between 2 Complex Numbers

Midpoint between 2 Complex Numbers
The Goal: Find the center point between them on the complex plane.
Key Concept: Applying the midpoint formula \(\left(\frac{a_1+a_2}{2} + \frac{b_1+b_2}{2}i\right)\).
Best for: Understanding the spatial relationships between different complex values.
Play now: Midpoint between 2 Complex Numbers

More Complex Number Worksheets Printable
Add & Subtract Complex Numbers
Multiply Complex Number
Rationalize Complex Number
Operations with Complex Numbers
Quadratic Equation with Complex Solutions

Online
Powers of i: Positive Exponents
Powers of i: Negative Exponents
Complex Number Addition
Complex Number Subtraction
Complex Number Multiplication
Complex Number Division

Complex Number: Magnitude (Absolute Value)
Distance Between Two Complex Numbers
Midpoint of Two Complex Numbers

Try out our new and fun Fraction Concoction Game.

Add and subtract fractions to make exciting fraction concoctions following a recipe. There are four levels of difficulty: Easy, medium, hard and insane. Practice the basics of fraction addition and subtraction or challenge yourself with the insane level.

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