2.06 Operations of Complex Numbers

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

Answer:   $11+2i$  

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

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

Answer:   $-7+10i$  

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:   $42+46i$  

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:   $26\ -\ 66i$