# The expression 1 + 4 i 3 + 2 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 7E
To determine

## To evaluate: The expression 1+4i3+2i in the form of a+bi.

Expert Solution

The value of the expression 1+4i3+2i is 1113+1013i.

### Explanation of Solution

Obtain the complex conjugate of number 3+2i.

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

3+2i¯=3¯+2i¯=3¯+2¯(i¯)=32i[i¯=i]

Thus, the complex conjugate of the number 3+2i is 32i.

Multiply numerator and denominator of the expression 1+4i3+2i by the complex conjugate of the denominator 3+2i and simplify the expression as follows.

1+4i3+2i=1+4i3+2i(32i32i)=32i+12i(4i)(2i)32(2i)2=3+10i8i294i2=3+10i8(1)94(1)[i2=1]

Further simplified as,

1+4i3+2i=3+10i+89+4=11+10i13=1113+1013i

Thus, the value of the expression 1+4i3+2i is 1113+1013i.

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