Complex Numbers- Cartesian & find Modulus Argument

In the complex plane, the horizontal axis if referred to as the ____ axis and the vertical axis is called the _____ axis

• real, imaginary
• imaginary, real
• complex, standard
• standard, cartesian

Where is point C located?

• 2 + i

• -3

• 2i

• -1 - i

Tags

CCSS.HSN.CN.B.4

Find the right Argand's Diagram for z = 4 - 8i

• 
• 
• 
• 

What complex number is shown on the graph?

• (-2,-3)

• -2-3i

• 2-3i

• 3i-2

Tags

CCSS.HSN.CN.A.1

CCSS.HSN.CN.B.5

Match the expression to the graph shown in the complex plane.

• (4,0)

• 4 + 4i

• -4(i²)

• 4i

Tags

CCSS.HSN.CN.A.1

CCSS.HSN.CN.A.2

CCSS.HSN.CN.B.4

CCSS.HSN.CN.B.5

Simplify:
(2 - 3i)(5 + 4i)

• 22 - 7i
• 22 + 7i
• 22 - 7i²
• 22 + 7i²

Tags

CCSS.HSN.CN.A.1

CCSS.HSN.CN.A.2

What is the complex conjugate of 4-3i?

• A. 1/(4-3i)

• B. 1/(4+3i)

• C. -4 + 3i

• D. 4 + 3i

Answer explanation

A conjugate of a complex number will have the same terms and an opposite +/- between them:

x = a + bi and it's conjugate is x = a - bi

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

One solution to the equation  $x^2+px+q=0$   is x = 1 + 4i. What would the factored form (x - m)(x - n)=0 of the quadratic be?

•  $(X-(1+4i))(X-(1-4i))\ =0$   
  

•  $(X+(1+4i))(X+(1-4i))=0$  

•  $(X-(1+4i))(X-(1+4i))=0$  

•  $(X-(1-4i))(X-(1-4i))=0$  

Answer explanation

Factored form is (x - m)(x - n) = 0, where m and n are solutions (aka x-values) that make the equation equal zero.
If one solution is x = 1 +4i, then you plug that in for m. 
The other solution will be the conjugate x = 1 -4i and you plug that in for n.
 $(X-(1-4i))(X-(1-4i))=0$  

One solution to the equation  $x^2+px+q=0$   is x = 1 + 4i. You determine the factored form to be 

 $(X-(1+4i))(X-(1-4i))\ =0$  
Use this to determine the standard form.

•  $x^2-2x+1-16i^2=0$  
  

•  $x^2-2x+17=0$  
  

• 17

•  $x^2+2x+1+8xi+4i-16i^2=0$  
  

Answer explanation