Imaginary and Complex Numbers

Simplifying Complex and imaginary Numbers

SWBAT: Define and use imaginary and complex numbers. Solve quadratic equations with complex roots.

Complex and imaginary Numbers: Simplifying

• An imaginary number is a real number multiplied by the imaginary unit i, which is defined by its property i² = −1

​Multiplying Complex Numbers

​When Multiplying Complex Numbers, use the same procedures used when multiplying Polynomials.

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​You may need to use the Distributive Property or Foil.

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​Remember that i² = -1

Multiple Choice

$$\left(2+3i\right)\times\left(3+7i\right)$$  

• $$6+21i^{ }$$  

• $$-15+23i$$  

Multiple Choice

Multiply: 
(4 – 3i)(-7 – 2i)

• A.  -23 + 13i
• B.  -23 - 29i
• C.  -34 + 13i
• D.  -34 - 29i

Multiple Choice

Multiply:
(2-5i)(2+5i)

• 29
• 4 - 25i
• 25 - 10i
• -21

Multiple Choice

$$Simplify:\ \ \ \ 2i\left(4\ +\ 3i\right)$$  

• $$-6\ +\ 8i$$  

• $$6\ +\ 8i$$  

• $$-6i\ +\ 8i$$  

• $$-1\ +\ 8i$$  

Multiple Choice

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Multiple Choice

Multiply/simplify the expression $$\left(3\ +\ 4i\right)\left(3\ +\ 4i\right)$$  

• $$-7\ +\ 24i$$  

• $$-25\ +\ 24i$$  

• $$7\ +24i$$  

• $$25\ +24i$$  

Multiple Choice

$$Simplify:\ \ \left(-2\ +\ 7i\right)\left(4\ -\ 2i\right)$$  

• $$6+\ 32i$$  

• $$-6\ +\ 32i$$  

• $$22+32i$$  

• $$6\ +\ 24i$$  

Multiple Choice

$$\left(7-5i\right)\left(7+5i\right)$$  

• 74

• 75

• 74+i

• 75-i