Complex numbers workshop

About this app

Every representation and operation of complex numbers in one place: drag z and w in the complex plane and read or type the Cartesian, polar and Euler forms live. The angle trap shows where arctan(b/a) lands in the wrong quadrant. Addition shifts, multiplication rotates and stretches the whole plane, division rotates back, conjugation mirrors, powers form a spiral and roots a regular n-gon. Each result shows the Cartesian and the polar calculation side by side and marks the easier one. The ‘One number’ mode shows the building blocks of the conversion for a single z (legs a and b, pointer r, angle φ, unit circle) and converts step by step between Cartesian, polar and Euler form.

Subject: Complex numbers

More from Complex numbers

• Euler's formula from the Taylor series
• Complex addition
• Complex division
• Complex multiplication
• n-th roots
• Powers of complex numbers
• Number system ladder: from ℕ to ℂ

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