Imaginary and Complex Numbers

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What is an imaginary number?

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What is the definition of a complex number?

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What is the product of two complex numbers (a + bi)(c + di)?

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The product is given by: (a + bi)(c + di) = ac + adi + bci + bdi^2 = (ac - bd) + (ad + bc)i.

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What is the conjugate of a complex number a + bi?

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The conjugate of a complex number a + bi is a - bi.

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How do you add two complex numbers?

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To add two complex numbers, simply add their real parts and their imaginary parts separately: (a + bi) + (c + di) = (a + c) + (b + d)i.

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What is the result of subtracting two complex numbers (a + bi) - (c + di)?

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The result is (a - c) + (b - d)i.

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What is the modulus of a complex number a + bi?

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How do you multiply a complex number by a real number?

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To multiply a complex number by a real number, multiply the real part and the imaginary part by that real number: k(a + bi) = ka + kbi.