The Complex Plane

Complex Numbers

Learning Target: I can simplify expressions with complex numbers.

Adding Complex Numbers

• When adding complex numbers

  -Add real parts together

  -Add imaginary parts together

Multiple Choice

Find the Sum

3i + 2i

• 5i

• 5i²

• 6i

• -5

Adding/Subtracting Complex Numbers

• Combine real terms

• Combine imaginary components

• Distribute negative first (when subtracting)

Multiple Choice

(4+7i)+(8-2i)=

• 34i

• 28+6i

• 12+5i

• -4+9i

Multiple Choice

(3-2i)-(4-2i)=

• -1+0i

• 7-4i

• 1-2i

• -i

Multiple Choice

(5+8i)+(6-10i)

• -1-18i

• 11-2i

• 13-4i

• -20i

Multiple Choice

(-9-5i)-(2-7i)

• -40+14i

• -7-12i

• -59i

• -11+2i

Multiplying Complex Numbers

• Remember to FOIL

• i²=-1

• Simplify as much as possible.

Multiple Choice

(2-i)(3+i)

• 5-i

• 7

• 7-i

Multiple Choice

(4+i)(5+i)

• 20+i

• 19+9i

• 9i

Multiple Choice

(3-4i)(2+i)

• -12+2i

• -24i

• 10-5i

​Complex Conjugates

Multiple Choice

Recall that the value of  $$i=\sqrt{-1}$$   . What is the value of  $$i^2$$  ?

• 1

• -1

• 2

• 0

Multiple Choice

Simplify the expression: $$i\left(i+2\right)$$  

• $$i+2i$$  

• $$-1+2i$$  

• 3

Multiple Choice

Simplify the expression:
$$\left(1+2i\right)\left(1-2i\right)$$  

Hint: Use the distributive property!

• $$1-4i^2$$  

• $$2$$  

• $$5$$  

Multiple Choice

Identify the complex conjugate:

$$1+2i$$  

• $$1+2i$$  

• $$1-2i$$  

• $$i^2$$  

• $$-1+2i$$  

Multiple Choice

Identify the complex conjugate:

$$2-3i$$  

• $$2+3i$$  

• $$2-3i$$  

• $$i^2$$  

• $$-2-3i$$  

Why the complex conjugate?

Why the complex conjugate?

Multiple Choice

Simplify.

$$\left(3-2i\right)\div\left(-2-2i\right)$$  

• $$\frac{7+4i}{5}$$  

• $$\frac{-3+2i}{5}$$  

• $$\frac{-1+5i}{4}$$  

• $$\frac{3i+2}{2}$$  

Multiple Choice

Simplify.

$$\left(-1+2i\right)\div\left(-3+4i\right)$$  

• $$\frac{-12-16i}{25}$$  

• $$\frac{11-2i}{25}$$  

• $$\frac{-6i+8}{25}$$  

• $$\frac{2-14i}{25}$$  

Multiple Choice

Simplify.

$$\left(3i\right)\div\left(4-3i\right)$$  

• $$\frac{12i-9}{25}$$  

• $$\frac{3i-9}{10}$$  

• $$\frac{24+18i}{25}$$  

• $$\frac{12+9i}{25}$$  

Multiple Choice

What complex number is represented by the graph?

• -3-i
• -3+i
• 1+3i
• 1-3i

Multiple Choice

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

• -2i-3i

• (0,-5)

• -6i

• -2(3i)

Multiple Choice

Where is point B located?

• 2 + i

• -3

• 2i

• -1 - i

Multiple Choice

Where is point C located?

• 2 + i

• -3

• 2i

• -1 - i

Multiple Choice

Where is point A located?

• 2 + i

• -3

• 2i

• -1 - i

Multiple Choice

What complex number is represented by the graph?

• -3-i
• -3+i
• 1+3i
• 1-3i

Multiple Choice

$$\left|3-2i\right|=\ ----$$  

• $$\sqrt{-13}$$  

• $$\sqrt{-1}$$  

• $$\sqrt{13}$$  

• $$5$$  

Multiple Choice

 Find modulus of z: 

$$z=1+3i$$

• $$\sqrt{10}$$  

• $$9-i$$  

• $$\sqrt{7}$$  

• $$4$$  

Multiple Choice

Calculate the value of modulus for $$-4+3i$$  

• $$-5$$  

• $$5$$  

• $$5i$$  

• $$-5i$$  

Multiple Choice

Simplify: $$\left|-1-5i\right|$$  

• $$1+5i$$  

• $$\sqrt{26}$$  

• $$\sqrt{6}$$  

• $$6i$$  

Multiple Choice

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

Multiple Choice

Determine the value of $$Z_1$$  

• $$3-6i$$  

• $$6-3i$$  

• $$6+3i$$  

• $$3+6i$$