Which description best defines Cartesian form of a complex number?

Which description best defines Cartesian form of a complex number?

• A. The equation given in terms of coordinates relative to the x, y axes
• B. The equation given in terms of polar coordinates
• C. The equation z = re^{i theta}
• D. The equation in terms of real numbers only

Answer: (A)

Cartesian form describes a complex number by its rectangular coordinates in the complex plane. It writes z as x + i y, where x is the real part and y is the imaginary part, giving the position (x, y) relative to the x-axis and y-axis. This is exactly what it means to use coordinates on the axes. The polar form would use r and θ, or z = r e^{iθ}, and the idea of “real numbers only” misses the imaginary part represented by i.

Cartesian form describes a complex number by its rectangular coordinates in the complex plane. It writes z as x + i y, where x is the real part and y is the imaginary part, giving the position (x, y) relative to the x-axis and y-axis. This is exactly what it means to use coordinates on the axes. The polar form would use r and θ, or z = r e^{iθ}, and the idea of “real numbers only” misses the imaginary part represented by i.