Complex Numbers

Complex numbers represent a fascinating aspect of mathematics, comprising both a real component and an imaginary component. Usually presented in the format 'a + bi', 'a' signifies the real component, while 'b' indicates the imaginary component, with 'i' symbolizing the square root of -1. Complex numbers play a pivotal role in higher-level mathematics and physics.

Complex Operations

Given a complex number z=5+3i, find the magnitude and argument of z.

Rationalizing with Complex Conjugates

Find the result of the following operation: 2+3i12i. Then, rationalize the denominator using complex conjugates.

Trigonometric Form of a Complex Number

Express the complex number z=3+4i in trigonometric form.

Finding the Complex Conjugate

Given the complex number z=4+3i, find the complex conjugate of z and then multiply z with its complex conjugate.

Finding the Magnitude of a Complex Number

Find the magnitude of the complex number z=3+4i