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7.3 Homework Problems: Multiplying and Dividing Complex Numbers in Rectangular Format

1. Multiply the following complex numbers

a.  [latex]\left(2+2i\right)\cdot\left(3+3i\right)[/latex]

b.  [latex]\left(5+0i\right)\cdot\left(2\ -\ 6i\right)[/latex]

c.  [latex]\left(3\ -\ 5.67i\right)\cdot\left(3.45+2.1i\right)[/latex]

d.  [latex]\left(\theta+\ \beta i\right)\cdot\left(\theta+\beta i\right)[/latex]

e.  [latex]\left(-2+6i\right)\cdot\left(-3\ -\ 6i\right)[/latex]

f.  [latex]\left(\sqrt{-7}\right)\cdot\left(\sqrt{-7}\right)[/latex]

g.  [latex]\left(\sqrt{-3}\right)\cdot\left(\sqrt{10}\right)[/latex]

 

2. Divide the following complex numbers

a.  [latex]\left(\sqrt{-27}\right)\div\left(\sqrt{-3}\right)[/latex]

b.  [latex]\left(2\ +\ 3i\right)\div\left(3\ +\ 4i\right)[/latex]

c.  [latex]\left(5\ -\ 6i\right)\div\left(7\ +\ 5i\right)[/latex]

d.  [latex]\left(1\right)\div\left(1\ +\ i\right)[/latex]

e.  [latex]\left(3i\right)\div\left(2\ +\ 3i\right)[/latex]

f.  [latex]\left(R\ +\ (mw)i\right)\div\left(R\ -\ (mw)i\right)[/latex]

g.  [latex]\left(a\ +\ bi\right)\div\left(a\ -\ bi\right)[/latex]

 

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