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Chapter 31: Chapter 31

Problem 1004

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Write each of the following in the form a \(+\) bi. (a) \((2+4 i)+(3+i)\) (b) \((2+i)-(4-2 i)\) (c) \((4-i)-(6-2 i)\) (d) \(3-(4+2 i)\)

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(a) \(5+5i\) (b) \(-2+3i\) (c) \(-2+i\) (d) \(-1-2i\)
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TABLE OF CONTENTS :
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Step 1: (a) Simplify and write in standard form: (2+4i)+(3+i)

First, we will simplify the expression by combining like terms: the real parts and the imaginary parts. We will do this by adding the real and imaginary parts separately. \[ (2+4i)+(3+i) = (2+3) + (4i+i) = 5+5i \] So, the simplified form of the expression is \(5+5i\).

Step 2: (b) Simplify and write in standard form: (2+i)-(4-2i)

First, we will simplify this expression by subtracting the real and imaginary parts separately. \[ (2+i)-(4-2i) = (2-4) + (i-(-2i)) = -2+3i \] So, the simplified form of the expression is \(-2+3i\).

Step 3: (c) Simplify and write in standard form: (4-i)-(6-2i)

First, we will simplify this expression by subtracting the real and imaginary parts separately. \[ (4-i)-(6-2i) = (4-6) + (-i-(-2i)) = -2+i \] So, the simplified form of the expression is \(-2+i\).

Step 4: (d) Simplify and write in standard form: 3-(4+2i)

First, we will simplify this expression by subtracting the real and imaginary parts separately. \[ 3-(4+2i) = (3-4) - 2i = -1-2i \] So, the simplified form of the expression is \(-1-2i\).

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