2.06 Operations of Complex Numbers

2.06 Operations of Complex Numbers

I can simplify expressions with complex numbers.

Add Complex Numbers

Simplify  $\left(2+6i\right)+\left(9-4i\right)$   

• Combine like terms:   $2+9$      $6i-4i$  

• Answer:   $11+2i$  

Subtract Complex Numbers

Simplify $\left(2+6i\right)-\left(9-4i\right)$  

• Distribute the minus sign:   $2+6i-9+4i$  

• Combine like terms:   $2-9$  and  $6i+4i$  

• Answer:   $-7+10i$  

Multiply Complex Numbers

Simplify  $\left(2+6i\right)\left(9-4i\right)$  

• Distribute 2 to both terms in the second binomial:   $2\cdot9\ +\ 2\cdot\left(-4i\right)\ \ or\ \ 18-8i$  

• Distribute 6i to both terms in the second binomial:   $6i\cdot9\ \ +\ 6i\cdot\left(-4i\right)\ \ or\ \ 54i\ -\ 24i^2\$  

• Recall  $i^2=-1$  : $54i\ -\ 24i^2\ =\ 54i\ -\ 24\left(-1\right)\ =54i\ +\ 24$ 

• Combine like terms:   $18+24$   +   $-8i+54i$  or   $42\ +46i$  

• Answer:   $42+46i$  

Simplify  $\left(5-7i\right)\left(8-2i\right)$  

• Distribute 5 to both terms in the second binomial:   $5\cdot8\ +\ 5\cdot\left(-2i\right)$  or   $40\ -\ 10i$  

• Distribute -7i to both terms in the second binomial:   $-7i\cdot8\ +\ -7i\cdot\left(-2i\right)$  or   $-56i\ +\ 14i^2$  

• Recall  $i^2=-1$  :   $-56i\ +\ 14\left(-1\right)$  or   $-56i\ -\ 14$  

• Combine like terms:   $40\ -\ 14$   +   $-10i\ -\ 56i$  or   $26\ -\ 66i$  

• Answer:   $26\ -\ 66i$  

Multiple Choice

 $\left(-2+5i\right)\left(8-3i\right)$  

Simplify

•  $21+35i$  

•  $-1+46i$  

•  $-9+46i$  

•  $-16+13i$