2023 - 2024 - Complex Numbers Operations

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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 i² = -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 conjugate of a complex number?

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The conjugate of a complex number a + bi is a - bi. It reflects the number across the real axis in the complex plane.

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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 + bdi². Remember that i² = -1.

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What is the modulus of a complex number?

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How do you divide two complex numbers?

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To divide (a + bi) by (c + di), multiply the numerator and denominator by the conjugate of the denominator: (a + bi)/(c + di) = [(a + bi)(c - di)]/[(c + di)(c - di)].

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