Understanding and applying conjugates of complex numbers

What is the conjugate of 3 - 2i?

• 2-3i

• 3-2i

• 3+2i

• 2+3i

 $z\ ,\ z_{1_{ }\ }and\ z_2\$  are complex number , then  $\overline{z_1-z_2}\ =\ \overline{z_1}\ -\ \overline{z_2}$  

• True

• False

Let's say you're solving a quadratic using the quadratic formula, and determine that one solution is x = 3 + 2i. What is the other solution?

• x = 3 + 2i

• x = 3 - 2i

• x = 3 + 2

• x = 3i + 2

Answer explanation

Every quadratic with complex solutions will have solutions in conjugate pairs:

x = a + bi and x = a - bi

If one solution is x = 3 + 2i, then the other solution will be x = 3 - 2i

The multiplicative inverse of  $3\ +4i\ =$  

•  $\frac{3}{25}-\frac{4}{25}i$  

•  $\frac{3}{25}\ +\ \frac{4}{25}i$  

•  $\frac{3}{7}+\frac{4}{7}i$  

•  $\frac{3}{7}-\frac{4}{7}i$  

What is the conjugate of 5i?

Imagine you are watching a cartoon where a magical character casts a spell to calculate the conjugate of a complex number. The number he uses is (-5 - 2i). What would be the result of his spell?

• -5 + 2i

• 5 - 2i

• -5 - 2i

• 5 + 2i

Calculate the inverse of  $-8-8i$  

•  $-\frac{1}{8}-\frac{1}{8}i$ 

•  $\frac{1}{8}+\frac{1}{8}i$ 
  

•  $-\frac{1}{16}-\frac{1}{16}i$ 
  

•  $-\frac{1}{16}+\frac{1}{16}i$ 
  

•  $\frac{1}{16}+\frac{1}{16}i$ 
  

Identify the complex conjugate of (-4-i)

• (4 - i)

• (-4 + i)

• (-4 - i)

• (4 + i)