Complex Numbers

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What is a complex number?

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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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What is the real part of a complex number?

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The real part of a complex number a + bi is the value 'a', which is a real number.

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What is the imaginary part of a complex number?

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The imaginary part of a complex number a + bi is the value 'b', which is a real number multiplied by the imaginary unit 'i'.

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How do you add two complex numbers?

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To add two complex numbers, 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 two complex numbers?

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To subtract two complex numbers, 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 complex conjugate of a complex number?

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The complex 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 two complex numbers?

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To multiply two complex numbers (a + bi) and (c + di), use the distributive property: (a + bi)(c + di) = ac + adi + bci + bdi^2. Remember that i^2 = -1.

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What is the modulus of a complex number?

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What is the argument of a complex number?

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