Understanding and applying conjugates of complex numbers

Given that $z=\frac{1}{2-3i}$  can be written as  $z=a+bi$ . Find  $a$  and  $b$  . 

•  $a=\frac{2}{13},\ b=\frac{3}{13}$  

•  $a=2,\ b=3$  

•  $a=-\frac{2}{5},\ b=-\frac{3}{5}$  

•  $a=-2,\ b=-3$  

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CCSS.HSN.CN.A.3

• A
• B
• C
• D

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CCSS.HSN.CN.A.3

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CCSS.HSN.CN.A.3

3/(4 - i)

• 9i

• -3 +12i

• (12 - 3i) / 4- i

• (12 + 3i) /17

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CCSS.HSN.CN.A.3

Calculate:

• 12/5 − 4/5i
• -8/10i − 4/5 
• -4/5 + 12/5i
• 12/5 + 4/5i

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CCSS.HSN.CN.A.3

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CCSS.HSN.CN.A.3

Simplify

• (-10+6i)/17
• (-8+15i)/17
• (-23+36i)/25
• (-21+33i)/34

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CCSS.HSN.CN.A.3

Simplify:   $\frac{\sqrt{-24}}{8}$  

•  $i\sqrt{3}$  

•  $\frac{i\sqrt{6}}{4}$  

•  $\frac{i\sqrt{6}}{2}$  

•  $\frac{6i\sqrt{2}}{8}$  

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CCSS.HSN.CN.A.3

Solve for this complex number conjugate:
 $\frac{3}{7+2i}$  

•  $\frac{20-6i}{53}$  

•  $\frac{21-8i}{54}$  
  

•  $\frac{21-6i}{53}$ 

•  $\frac{8i-21}{53}$  
  

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CCSS.HSN.CN.A.3

 $z\ ,\ z_{1_{ }\ }and\ z_2\$  are colmlex number , then  $\left(\overline{\frac{z_1}{z_2}}\ \right)\ =\ \frac{\overline{z_1}}{\overline{z_2}}\$  , $z_2\ne0$  

• False

• True

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CCSS.HSN.CN.A.3