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.

Finding All Complex Number Solutions

Find all complex number solutions for the equation

z^{4} = 16

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Find the Roots of a Complex Number

Find all the roots of the complex number

z = 8 (c o s (\frac{π}{3}) + i s i n (\frac{π}{3}))

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Complex Operations

\frac{12 cis (\frac{8}{3} π)}{11 cis (\frac{12}{11} π)}

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Rationalizing with Complex Conjugates

Let

z = 1 + i \sqrt{3}

. Compute

\frac{z}{1 - z}

and simplify the result.

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Trigonometric Form of a Complex Number

\frac{4 cis (152^{\circ})}{3 cis (108^{\circ})}

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Finding the Complex Conjugate

Find the complex conjugate of the complex number

z = 3 \cos θ + 3 i \sin θ

where

θ = \frac{π}{6}

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Finding the Magnitude of a Complex Number

Find the magnitude of the complex number

z = 3 \cos (θ) + 3 i \sin (θ)

where

θ = \frac{π}{4}

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Complex Numbers

Finding All Complex Number Solutions

Find the Roots of a Complex Number

Complex Operations

Rationalizing with Complex Conjugates

Trigonometric Form of a Complex Number

Finding the Complex Conjugate

Finding the Magnitude of a Complex Number

Popular Problems