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Multivariable Calculus

8th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781305266643
BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781305266643
Chapter G, Problem 8E
Textbook Problem
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Evaluate the expression and write your answer in the form a + bi.

8. 3 + 2 i 1 4 i

To determine

To evaluate: The expression 3+2i14i in the form of a+bi.

Explanation of Solution

Obtain the complex conjugate of number 14i.

Use the property of conjugates z+w¯=z¯+w¯ and zw¯=z¯w¯ to simplify the expression as follows.

14i¯=1¯4i¯=1¯(4¯(i¯))=1+4i[i¯=i]

Thus, the complex conjugate of the number 14i is 1+4i.

Multiply numerator and denominator of the expression 3+2i14i by the complex conjugate of the denominator 14i and simplify the expression as follows

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Chapter G Solutions

Multivariable Calculus
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Ch. G - Evaluate the expression and write your answer in...Ch. G - Evaluate the expression and write your answer in...Ch. G - Evaluate the expression and write your answer in...Ch. G - Evaluate the expression and write your answer in...Ch. G - Find the complex conjugate and the modulus of the...Ch. G - Find the complex conjugate and the modulus of the...Ch. G - Find the complex conjugate and the modulus of the...Ch. G - Prove the following properties of complex numbers....Ch. G - Find all solutions of the equation. 19. 4x2 + 9 =...Ch. G - Find all solutions of the equation. 20. x4 = 1Ch. G - Find all solutions of the equation. 21. x2 + 2x +...Ch. G - Find all solutions of the equation. 22. 2x2 2x +...Ch. G - Find all solutions of the equation. 23. z2 + z + 2...Ch. G - Find all solutions of the equation. 24....Ch. G - Write the number in polar form with argument...Ch. G - Write the number in polar form with argument...Ch. G - Write the number in polar form with argument...Ch. G - Write the number in polar form with argument...Ch. G - Write the number in polar form with argument...Ch. G - Find polar forms for zw, z/w, and 1/z by first...Ch. G - Find polar forms for zw, z/w, and 1/z by first...Ch. G - Find polar forms for zw, z/w, and 1/z by first...Ch. G - Find the indicated power using De Moivres Theorem....Ch. G - Find the indicated power using De Moivres Theorem....Ch. G - Find the indicated power using De Moivres Theorem....Ch. G - Find the indicated power using De Moivres Theorem....Ch. G - Find the indicated roots. Sketch the roots in the...Ch. G - Find the indicated roots. Sketch the roots in the...Ch. G - Find the indicated roots. Sketch the roots in the...Ch. G - Find the indicated roots. Sketch the roots in the...Ch. G - Write the number in the form a + bi. 41. ei/2Ch. G - Write the number in the form a + bi. 42. e2iCh. G - Write the number in the form a + bi. 43. ei/3Ch. G - Write the number in the form a + bi. 44. eiCh. G - Write the number in the form a + bi. 45. e2+iCh. G - Write the number in the form a + bi. 46. e+iCh. G - Use De Moivres Theorem with n = 3 to express cos 3...Ch. G - Use Eulers formula to prove the following formulas...Ch. G - If u(x) = f(x) + ig(x) is a complex-valued...Ch. G - (a) If u is a complex-valued function of a real...

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