Working with 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 i^2 = -1.

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What is 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 product of two complex conjugates?

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The product of two complex conjugates (a + bi)(a - bi) is a^2 + b^2.

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What is the modulus of a complex number?

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How do you multiply two complex numbers?

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

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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'.

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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'.

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