Chapter 7 Note Packet
... Example 5: Rationalizing the Denominator Rationalize the denominator of each expression. Assume that all variables are positive. a ...
... Example 5: Rationalizing the Denominator Rationalize the denominator of each expression. Assume that all variables are positive. a ...
3 Complex Numbers
... Notice a difference though: In Section 2, we rotated the coordinate system, and the formulas (∗) expressed old coordinates of a vector via new coordinates of the same vector. This time, we transform vectors, while the coordinate system remains unchanged. The same formulas now express coordinates (X, ...
... Notice a difference though: In Section 2, we rotated the coordinate system, and the formulas (∗) expressed old coordinates of a vector via new coordinates of the same vector. This time, we transform vectors, while the coordinate system remains unchanged. The same formulas now express coordinates (X, ...
5. The algebra of complex numbers We use complex numbers for
... 5.3. The fundamental theorem of algebra. Complex numbers remedy a defect of real numbers, by providing a solution for the quadratic equation x2 + 1 = 0. It turns out that you don’t have to worry that someday you’ll come across a weird equation that requires numbers even more complex than complex num ...
... 5.3. The fundamental theorem of algebra. Complex numbers remedy a defect of real numbers, by providing a solution for the quadratic equation x2 + 1 = 0. It turns out that you don’t have to worry that someday you’ll come across a weird equation that requires numbers even more complex than complex num ...
5. The algebra of complex numbers We use complex
... ative real number, nonzero as long as z ∞= 0. Its nonnegative square root is the absolute value or modulus of z, written ...
... ative real number, nonzero as long as z ∞= 0. Its nonnegative square root is the absolute value or modulus of z, written ...
Fun With Complex Numbers
... Verify that when you write the vector for the complex number i, this definition of multiplication gives back i2 = −1. This justifies the existence of complex numbers: they are simply vectors in the plane that can be multiplied together using this formula. 6. Polar Forms Find the modulus, argument an ...
... Verify that when you write the vector for the complex number i, this definition of multiplication gives back i2 = −1. This justifies the existence of complex numbers: they are simply vectors in the plane that can be multiplied together using this formula. 6. Polar Forms Find the modulus, argument an ...
