Front

What is the definition of 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.

Front

What is the imaginary unit 'i'?

Back

Front

What is the standard form of a complex number?

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The standard form of a complex number is a + bi, where a is the real part and b is the imaginary part.

Front

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.

Front

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.

Front

What is the product of two complex numbers?

Back

To multiply two complex numbers (a + bi) and (c + di), use the distributive property: (a + bi)(c + di) = ac + adi + bci + bdi^2. Since i^2 = -1, the result simplifies to (ac - bd) + (ad + bc)i.

Front

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 used to simplify the division of complex numbers.

Front

How do you divide two complex numbers?

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To divide two complex numbers, multiply the numerator and denominator by the conjugate of the denominator. For example, to divide (a + bi) by (c + di), multiply by (c - di) to eliminate the imaginary part in the denominator.

Front

What is the modulus of a complex number?

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Front

What is the argument of a complex number?

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