Polar Form of Complex Numbers

Front

What is the polar form of a complex number?

Back

The polar form of a complex number is expressed as r(cos θ + i sin θ), where r is the modulus and θ is the argument.

Front

How do you find the modulus of a complex number z = a + bi?

Back

The modulus is found using the formula |z| = √(a² + b²).

Front

What is the argument of a complex number?

Back

The argument is the angle θ formed with the positive x-axis, calculated using θ = arctan(b/a).

Front

Convert the complex number -2 + 5i to polar form.

Back

5.39 (cos 1.95 + i sin 1.95).

Front

What is the rectangular form of a complex number in polar form r(cos θ + i sin θ)?

Back

The rectangular form is given by a + bi, where a = r cos θ and b = r sin θ.

Front

How do you multiply two complex numbers in polar form?

Back

Multiply their moduli and add their arguments: r1 * r2 (cos(θ1 + θ2) + i sin(θ1 + θ2)).

Front

What is the rectangular form of 4(cos π/3 + i sin π/3)?

Back

2 + 2√3 i.

Front

Find the modulus and quadrant of the complex number -3 + i.

Back

Modulus: √10, Quadrant: Quadrant 2.

Front

What is the significance of the angle in the polar form of a complex number?

Back

The angle indicates the direction of the complex number in the complex plane.

Front

How do you convert a complex number from rectangular to polar form?

Back

Calculate the modulus r = √(a² + b²) and the argument θ = arctan(b/a).