# The expression 3 4 − 3 i in the form of a + b i .

### Single Variable Calculus: Concepts...

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

### Single Variable Calculus: Concepts...

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

#### Solutions

Chapter I, Problem 10E
To determine

## To evaluate: The expression 34−3i in the form of a+bi.

Expert Solution

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.

### Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!