What is the imaginary unit $$i$$ ?

The imaginary unit $$i$$ is defined as $$\sqrt[]{-1}$$ .

What is the sum of a real number and an imaginary number?

The sum is a complex number, expressed as $$a + bi$$ .

How do you multiply two complex numbers, $$(a + bi)(c + di)$$ ?

Use the distributive property: $$ac + adi + bci + bdi^2 = (ac - bd) + (ad + bc)i$$ .

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

The modulus is $$\sqrt{a^2 + b^2}$$ .

What is the argument of a complex number?

The argument is the angle formed with the positive x-axis in the complex plane, often denoted as $$\theta$$ .

What is the polar form of a complex number?

The polar form is expressed as $$r(cos(\theta) + i sin(\theta))$$ , where $$r$$ is the modulus and $$\theta$$ is the argument.

What is the relationship between rectangular and polar forms of complex numbers?

Rectangular form is $$a + bi$$ , while polar form is $$r(cos(\theta) + i sin(\theta))$$ , where $$r = \sqrt{a^2 + b^2}$$ and $$\theta = \tan^{-1}(\frac{b}{a})$$ .

Complex Numbers Review Flashcards

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1.

FLASHCARD QUESTION

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6i

2.

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i

3.

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5i

4.

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5.

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6.

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Define a complex number.

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7.

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