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CalculusMultivariable Calculus8th Edition
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Evaluate the expression and write your answer in the form a + bi. 8. 3 + 2 i 1 − 4 i

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Multivariable Calculus

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

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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+2i1−4i in the form of a+bi.

Explanation of Solution

Obtain the complex conjugate of number 1−4i.

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

1−4i¯=1¯−4i¯=1¯−(4¯(i¯))=1+4i              [∵i¯=−i]

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

Multiply numerator and denominator of the expression 3+2i1−4i by the complex conjugate of the denominator 1−4i   and simplify the expression as follows

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