How do you add two complex numbers?

To add two complex numbers z1 = a + bi and z2 = c + di, you add their real parts and their imaginary parts: $$z1 + z2 = (a + c) + (b + d)i$$ .

How do you multiply two complex numbers?

To multiply two complex numbers z1 = a + bi and z2 = c + di, use the distributive property: $$z1 \times z2 = (ac - bd) + (ad + bc)i$$ .

What is the polar form of a complex number?

The polar form of a complex number z = a + bi is expressed as $$z = r(\text{cos}(\theta) + i\text{sin}(\theta))$$ , where r is the modulus and θ is the argument.

What is the modulus of a complex number?

The modulus of a complex number z = a + bi is given by $$|z| = \text{sqrt}(a^2 + b^2)$$ .

What is the argument of a complex number?

The argument of a complex number z = a + bi is the angle θ formed with the positive real axis, calculated as $$\theta = \text{tan}^{-1}(\frac{b}{a})$$ .

What is the relationship between complex numbers and the Cartesian plane?

Complex numbers can be represented as points in the Cartesian plane, where the x-axis represents the real part and the y-axis represents the imaginary part.

What is the significance of the imaginary unit 'i'?

The imaginary unit 'i' is significant because it allows for the extension of real numbers to complex numbers, enabling solutions to equations that do not have real solutions.

How do you find the square root of a complex number?

To find the square root of a complex number z = a + bi, convert to polar form and use $$\text{sqrt}(r)(\text{cos}(\frac{\theta}{2}) + i\text{sin}(\frac{\theta}{2}))$$ .

Complex numbers

Flashcard

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Mathematics

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University

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Practice Problem

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Hard

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CCSS

HSN.CN.A.1, HSN.CN.B.4, HSN.CN.A.3

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FLASHCARD QUESTION

Front

What is an imaginary number?

Back

Tags

CCSS.HSN.CN.A.1

FLASHCARD QUESTION

Front

What is a pure real number?

Back

A pure real number is a complex number where the imaginary part is zero, represented as z = a + 0i, where a is a real number.

Tags

CCSS.HSN.CN.A.1

FLASHCARD QUESTION

Front

What is the absolute value of a complex number z = α + iβ?

Back

FLASHCARD QUESTION

Front

What is the relationship between the exponential function and complex numbers?

Back

FLASHCARD QUESTION

Front

What is the logarithm of a complex number in the form of xi?

Back

FLASHCARD QUESTION

Front

What is Euler's formula?

Back

Tags

CCSS.HSN.CN.B.4

FLASHCARD QUESTION

Front

What is the conjugate of a complex number z = a + bi?

Back

Tags

CCSS.HSN.CN.A.3

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