Powers of i and Complex Numbers

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 i = √(-1).

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as the square root of -1, i.e., i = √(-1). It is used to represent imaginary numbers.

Front

How do you calculate the distance from the origin to a point in the complex plane?

Back

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Front

What is the polar form of a complex number?

Back

The polar form of a complex number is expressed as r(cos θ + i sin θ), where r is the modulus and θ is the argument of the complex number.

Front

How do you convert a complex number from rectangular form to polar form?

Back

Front

What is the conjugate of a complex number?

Back

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 (a + bi) and (c + di), combine the real parts and the imaginary parts: (a + c) + (b + d)i.

Front

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: (ac - bd) + (ad + bc)i.

Front

What is the modulus of a complex number?

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