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Problem 1004

# 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) $$-1-2i$$
See the step by step solution

## 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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