Polar Form of Complex Numbers

Trigonometry · Axiom Academy

LESSON Polar Form of Complex Numbers Understanding how complex numbers can be represented using magnitude and angle, and converting between rectangular and polar forms. Every complex number can be written as z = a + bi , where: a is the real part (horizontal component) b is the imaginary part (vertical component) i is the imaginary unit where i² = -1 The same complex number can be expressed using polar coordinates as z = r(cos θ + i sin θ) , where: r is the modulus (distance from origin) θ is the argument (angle from positive real axis) 3. Converting Rectangular to Polar Given a complex number z = a + bi, we can find its polar form using: 4. Converting Polar to Rectangular Given a complex number in polar form z = r(cos θ + i sin θ), we can find the rectangular form by evaluating the trigonometric functions: Try converting between forms! Enter values and see both representations visualized on the complex plane.

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