(a) To plot: The points corresponding to the given complex numbers .

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Answer 1

Question

System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

Chapter 12, Problem 40E

To determine

(a)

To plot:

The points corresponding to the given complex numbers.

To determine

(b)

To plot:

The points corresponding to the given complex numbers.

To determine

(c)

To explain:

Geometric effect does multiplication by −i have on a complex number.

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(a) Write the following expression in terms of i, perform multiplication, and simplify V=25 · V-125. Student solution. The first square root can be written in terms of i as: V-25 = The second square root can be written in terms of i as: V-125 =0 Lastly we obtain: V-25 · V-125 = (b) Compute the sum of the various powers of i: i48. 18 + i 49 +¿50 Student solution. The first power of i equals: 18 The second power of i equals: 49 - The third power of i equals: 50 The sum of these powers of i equals: 48 +

Express the following in a + ib form a. (41-7)+(2+i) b. (5-2i)(2+ 2i)

(a) Simplify the following: (ii) V-180 (b) For the complex numbers 21 = 8+ 15j and z2 =-3 + 8j, write out and simplify (i) 321 -222 (ii) z1.22 (ii) (iv) arg z1

Answer 2

Question

System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

Chapter 12, Problem 40E

To determine

(a)

To plot:

The points corresponding to the given complex numbers.

To determine

(b)

To plot:

The points corresponding to the given complex numbers.

To determine

(c)

To explain:

Geometric effect does multiplication by −i have on a complex number.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

Chapter 12, Problem 40E

To determine

(a)

To plot:

The points corresponding to the given complex numbers.

To determine

(b)

To plot:

The points corresponding to the given complex numbers.

To determine

(c)

To explain:

Geometric effect does multiplication by −i have on a complex number.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 4

Question

System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

Chapter 12, Problem 40E

To determine