Explanation Formula used: Let z 1 = r 1 ( cos θ 1 + i sin θ 1 ) and z 2 = r 2 ( cos θ 2 + i sin θ 2 ) polar form of the two complex number then, z 1 z 2 = r 1 r 2 [ cos ( θ 1 + θ 2 ) + i sin ( θ 1 + θ 2 ) ] , z 1 z 2 = r 1 r 2 [ cos ( θ 1 − θ 2 ) + i sin ( θ 1 − θ 2 ) ] where z 2 ≠ 0 and 1 z 1 = 1 r 1 [ cos θ 1 − i sin θ 1 ] Calculation: It is given that z = 4 3 − 4 i and w = 8 i . Rewrite the complex number z = 4 3 − 4 i and w = 8 i in polar form. The polar form of the complex number z = a + b i is z = r ( cos θ + i sin θ ) where r = | z | = a 2 + b 2 and tan θ = b a . Consider the complex number z = 4 3 − 4 i . Obtain the argument of the complex number z = 4 3 − 4 i . tan θ = − 4 4 3 = − 1 3 Thus, the argument of argument of the complex number z = 4 3 − 4 i is θ = tan − 1 ( − 1 3 ) = 11 π 6 Obtain the modulus of the complex number z = 4 3 − 4 i . r = | 4 3 − 4 i | = ( 4 3 ) 2 + ( − 4 ) 2 = 48 + 16 = 8 Thus, the value of r = 8 . Thus, the polar form of the complex number z = 4 3 − 4 i is 8 ( cos 11 π 6 + i sin 11 π 6 ) . Similarly, obtain the polar form of the complex number w = 8 i . The argument of argument of the complex number w = 8 i is, θ = tan − 1 ( 8 0 ) = tan − 1 ( ∞ ) = π 2 Thus, the argument of argument of the complex number w = 8 i is π 2

Single Variable Calculus: Early Transcendentals, Volume I

8th Edition

ISBN: 9781305842410

Author: James Stewart

Publisher: Cengage Learning US

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Chapter H, Problem 30E

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To find: The polar form of zw,zw and 1z by putting z and w in polar form.

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Chapter H, Problem 29E

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Chapter H Solutions

Single Variable Calculus: Early Transcendentals, Volume I

Ch. H - Prob. 1E Ch. H - Prob. 2E Ch. H - Prob. 3E Ch. H - Prob. 4E Ch. H - Prob. 5E Ch. H - Prob. 6E Ch. H - Prob. 7E Ch. H - Evaluate the expression and write your answer in...Ch. H - Prob. 9E Ch. H - Prob. 10E

Ch. H - Prob. 11E Ch. H - Prob. 12E Ch. H - Prob. 13E Ch. H - Evaluate the expression and write your answer in...Ch. H - Prob. 15E Ch. H - Prob. 16E Ch. H - Prob. 17E Ch. H - Prove the following properties of complex numbers....Ch. H - Prob. 19E Ch. H - Prob. 20E Ch. H - Prob. 21E Ch. H - Find all solutions of the equation. 22. 2x2 2x +...Ch. H - Prob. 23E Ch. H - Find all solutions of the equation. 24....Ch. H - Write the number in polar form with argument...Ch. H - Prob. 26E Ch. H - Prob. 27E Ch. H - Prob. 28E Ch. H - Write the number in polar form with argument...Ch. H - Prob. 30E Ch. H - Prob. 31E Ch. H - Prob. 32E Ch. H - Find the indicated power using De Moivres Theorem....Ch. H - Prob. 34E Ch. H - Prob. 35E Ch. H - Prob. 36E Ch. H - Prob. 37E Ch. H - Prob. 38E Ch. H - Prob. 39E Ch. H - Prob. 40E Ch. H - Prob. 41E Ch. H - Prob. 42E Ch. H - Prob. 43E Ch. H - Prob. 44E Ch. H - Prob. 45E Ch. H - Prob. 46E Ch. H - Prob. 47E Ch. H - Use Eulers formula to prove the following formulas...Ch. H - If u(x) = f(x) + ig(x) is a complex-valued...Ch. H - (a) If u is a complex-valued function of a real...

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The polar form of z w , z w and 1 z by putting z and w in polar form.

Solution Summary: The author explains the polar form of the complex number zw,zw, and fric1x by putting x and w in a

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To find: The polar form of zw,zw and 1z by putting z and w in polar form.

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Chapter H Solutions