Complex Number To Rectangular Form
Convert any complex number from polar form rangletheta to rectangular a+bi instantly. Free polar-to-rectangular conversion with real and imaginary parts, bar chart, and formula breakdown for students and engineers.
About This Calculator
Complex Number to Rectangular Form Calculator
This calculator converts complex numbers from polar form (magnitude r and angle theta) to rectangular form (a + bi). Simply enter the magnitude and angle in degrees, and the calculator instantly computes the real part a = r·cos(theta) and the imaginary part b = r·sin(theta). A bar chart visualizes the two components for quick comparison.
The polar-to-rectangular conversion is essential for students learning complex analysis, electrical engineers working with phasors, and anyone who needs to switch between the two common representations of complex numbers. Our calculator handles any real magnitude, positive or negative angles, and displays results with up to four decimal places for precision.
Frequently Asked Questions
How do you convert a complex number from polar to rectangular form?
To convert a complex number from polar form rangletheta to rectangular form a+bi, use the formulas a = r·cos(theta) for the real part and b = r·sin(theta) for the imaginary part, where theta is in radians. Our calculator converts degrees to radians automatically.
What is rectangular form of a complex number?
The rectangular form of a complex number is written as a + bi, where a is the real part and b is the imaginary part. It represents a point (a, b) on the complex plane with the horizontal axis representing real numbers and the vertical axis representing imaginary numbers.
What is the difference between polar and rectangular form?
Polar form expresses a complex number as rangletheta where r is the distance from the origin (magnitude) and theta is the angle counterclockwise from the positive real axis. Rectangular form expresses it as a+bi where a and b are Cartesian coordinates. Polar form is convenient for multiplication and division, while rectangular form is easier for addition and subtraction.
Can this calculator handle negative angles?
Yes, you can enter negative angles in degrees. A negative angle indicates a clockwise rotation from the positive real axis. The calculator correctly computes both real and imaginary parts using the standard trigonometric formulas.
How do I convert a complex number from rectangular to polar form?
To convert from rectangular form a+bi to polar form rangletheta, compute the magnitude r = sqrt(a^2+b^2) and the angle theta = arctan(b/a) in the appropriate quadrant. Use our Complex Number to Polar Form calculator for instant conversions in the reverse direction.
What are common applications of complex numbers in rectangular form?
Complex numbers in rectangular form are widely used in electrical engineering for AC circuit analysis (impedance, voltage, and current), signal processing (Fourier transforms), control systems, quantum mechanics, fluid dynamics, and computer graphics. The a+bi representation makes addition and subtraction of complex numbers straightforward.