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Precalculus: Mathematics for Calcu...

7th Edition
James Stewart + 2 others
Publisher: Brooks Cole
ISBN: 9781305071759
BuyFind

Precalculus: Mathematics for Calcu...

7th Edition
James Stewart + 2 others
Publisher: Brooks Cole
ISBN: 9781305071759

Solutions

Chapter
Section
Chapter 8.3, Problem 42E
Textbook Problem
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Polar Form of Complex Numbers Write the complex number in polar form with argument θ between 0 and 2π.

42. 5 15 i

Expert Solution
To determine

The polar form of the complex number 515i with argument θ between 0 and 2π .

Explanation of Solution

Given:

The below number is a complex number.

515i

Formula used: polar form

z=r(cosθ+isinθ) (I)

Where,

  • The number r is the modulus of z .
  • r=|z|=a2+b2 (II)
  • The θ is the argument of z .
  • tanθ=ba (III)

Calculation:

The general form of a complex number.

z=a+ib (IV)

The given complex number.

z=515i (V)

From equation (IV) and (V) the value of a is 5 and the value of b is 15 .

Substitute 5 for a and 15 for b in the equation (II) to find the value of r .

r=(5)2+(15)2=5+15=20=25

Substitute 5 for a and 15 for b in the equation (III) to find the value of θ

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Chapter 8 Solutions

Precalculus: Mathematics for Calculus (Standalone Book)
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Ch. 8.1 - Different Polar Coordinates for the Same Point...Ch. 8.1 - Different Polar Coordinates for the Same Point...Ch. 8.1 - Different Polar Coordinates for the Same Point...Ch. 8.1 - Different Polar Coordinates for the Same Point...Ch. 8.1 - Different Polar Coordinates for the Same Point...Ch. 8.1 - Different Polar Coordinates for the Same Point...Ch. 8.1 - Points in Polar Coordinates Determine which point...Ch. 8.1 - Points in Polar Coordinates Determine which point...Ch. 8.1 - Points in Polar Coordinates Determine which point...Ch. 8.1 - Points in Polar Coordinates Determine which point...Ch. 8.1 - Points in Polar Coordinates Determine which point...Ch. 8.1 - Points in Polar Coordinates Determine which point...Ch. 8.1 - Points in Polar Coordinates Determine which point...Ch. 8.1 - Points in Polar Coordinates Determine which point...Ch. 8.1 - Rectangular Coordinates to Polar Coordinates A...Ch. 8.1 - Rectangular Coordinates to Polar Coordinates A...Ch. 8.1 - Polar Coordinates to Rectangular Coordinates A...Ch. 8.1 - 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(a)...Ch. 8 - Complex Numbers A complex number is given. (a)...Ch. 8 - Complex Numbers A complex number is given. (a)...Ch. 8 - Complex Numbers A complex number is given. (a)...Ch. 8 - Complex Numbers A complex number is given. (a)...Ch. 8 - Complex Numbers A complex number is given. (a)...Ch. 8 - Powers Using De Moivres Theorem Use De Moivres...Ch. 8 - Powers Using De Moivres Theorem Use De Moivres...Ch. 8 - Powers Using De Moivres Theorem Use De Moivres...Ch. 8 - Powers Using De Moivres Theorem Use De Moivres...Ch. 8 - Roots of Complex Numbers Find the indicated roots....Ch. 8 - Roots of Complex Numbers Find the indicated roots....Ch. 8 - Roots of Complex Numbers Find the indicated roots....Ch. 8 - Roots of Complex Numbers Find the indicated roots....Ch. 8 - Parametric Curves A pair of parametric equations...Ch. 8 - Parametric Curves A pair of parametric equations...Ch. 8 - Parametric Curves A pair of parametric equations...Ch. 8 - Parametric Curves A pair of parametric equations...Ch. 8 - Graphs of Parametric Equations Use a graphing...Ch. 8 - Graphs of Parametric Equations Use a graphing...Ch. 8 - Finding Parametric Equations for a Curve In the...Ch. 8 - (a) Convert the point whose polar coordinates are...Ch. 8 - (a) Graph the polar equation r = 8 cos . What type...Ch. 8 - Graph the polar equation r = 3 + 6 sin . What type...Ch. 8 - Let z=1+3i. (a) Graph z in the complex plane. (b)...Ch. 8 - Let z1=4(cos712+isin712) and z2=2(cos512+isin512)....Ch. 8 - Find the cube roots of 27i, and sketch these roots...Ch. 8 - (a) Sketch the curve represented by the parametric...Ch. 8 - Find parametric equations for the line of slope 2...Ch. 8 - The position of an object in circular motion is...Ch. 8 - Trajectories Are Parabolas From the graphs in...Ch. 8 - Path of a Baseball Suppose a baseball is thrown at...Ch. 8 - Path of a Rocket Suppose that a rocket is fired at...Ch. 8 - Firing a Missile The initial speed of a missile is...Ch. 8 - Maximum Height Show that the maximum height...Ch. 8 - Shooting into the Wind Suppose that a projectile...Ch. 8 - Shooting into the Wind Using the parametric...

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