BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter I, Problem 10E
To determine

To evaluate: The expression 343i in the form of a+bi.

Expert Solution

Answer to Problem 10E

The value of the expression 343i is 1225+925i.

Explanation of Solution

Obtain the complex conjugate of number 43i.

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

43i¯=4¯3i¯=4¯(3¯(i¯))=4+3i[i¯=i]

Thus, the complex conjugate of the number 43i is 4+3i.

Multiply numerator and denominator of the expression 343i by the complex conjugate of the denominator 14i and simplify the expression as follows.

343i=343i(4+3i4+3i)=12+9i42(3i)2=12+9i169i2=12+9i169(1)[i2=1]

Further simplified as,

3+2i14i=12+9i25=1225+925i

Thus, the value of the expression 343i is 1225+925i.

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