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 \( z \).
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Rationalizing with Complex Conjugates

Find the result of the following operation: \(\frac{2 + 3i}{1 - 2i}\). Then, rationalize the denominator using complex conjugates.
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Trigonometric Form of a Complex Number

Express the complex number \(z = -3 + 4i\) in trigonometric form.
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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.
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Finding the Magnitude of a Complex Number

Find the magnitude of the complex number \(z = 3 + 4i\)
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Popular Problems

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