Front

What is a complex number?

Back

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit, defined as the square root of -1.

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What is the imaginary unit 'i'?

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The imaginary unit 'i' is defined as the square root of -1. It is used to extend the real number system to include solutions to equations that do not have real solutions.

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How do you add complex numbers?

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To add complex numbers, you add their real parts and their imaginary parts separately. For example, (a + bi) + (c + di) = (a + c) + (b + d)i.

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How do you subtract complex numbers?

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To subtract complex numbers, you subtract their real parts and their imaginary parts separately. For example, (a + bi) - (c + di) = (a - c) + (b - d)i.

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What is the modulus of a complex number?

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The modulus of a complex number a + bi is given by the formula |a + bi| = √(a² + b²). It represents the distance of the complex number from the origin in the complex plane.

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What is the conjugate of a complex number?

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The conjugate of a complex number a + bi is a - bi. It is obtained by changing the sign of the imaginary part.

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How do you multiply complex numbers?

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To multiply complex numbers, use the distributive property (FOIL method). For example, (a + bi)(c + di) = ac + adi + bci + bdi², and since i² = -1, combine like terms.

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What is the significance of the end behavior of a function involving complex numbers?

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The end behavior of a function describes how the function behaves as the input approaches positive or negative infinity. It helps in understanding the limits and asymptotic behavior of complex functions.

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What is the solution to the equation x² = 16?

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The solutions to the equation x² = 16 are x = ±4, which means x can be either 4 or -4.

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What does it mean for a complex number to be in standard form?

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A complex number is in standard form when it is expressed as a + bi, where a is the real part and b is the imaginary part.