Complex Numbers Operations

If a circuit has a current I = 3 + 2i and a resistance Z = 2 - i, what is the voltage of the circuit?

What is the additive inverse of the complex number -8 + 3i?

Which equation shows an example of the associative property of addition?

Which property of multiplication is shown: If x = a + bi and y = c + di, x × y = y × x?

Which property of addition is shown: a + bi + c + di = a + c + bi + di?

What mistake did Donte make in simplifying the expression 4(1 + 3i)?

If Melissa has a score of 5 - 4i and Tomas has a score of 3 + 2i, what is their total score?

Which property of addition is shown: If x = a + bi and y = -a - bi, x + y = 0?

What is the value of the product (3 - 2i)(3 + 2i)?

Which equation demonstrates the additive identity property?

Operations with Complex Numbers

The relationship between voltage (E), current (I), and resistance (Z) is expressed as E = IZ.
Example: For I = 3 + 2i and Z = 2 - i, the voltage E is calculated to be 8 + i.

Additive Inverse

The additive inverse of a complex number reverses its sign.
For -8 + 3i, the additive inverse is 8 - 3i.

Associative Property of Addition

This property showcases that the way numbers are grouped in addition does not affect the sum.
Example: (-4 + i) + 4i equals -4 + (i + 4i).

Commutative Property of Multiplication

Indicates that the order of factors does not change the product.
For any complex numbers x = a + bi and y = c + di, x × y = y × x illustrates this property.

Commutative Property of Addition

Similar to multiplication, the order of addends does not affect the sum.
Example: a + bi + c + di can be rearranged to a + c + bi + di.

Distributive Property Mistake

An example of incorrect application of the distributive property.
Donte incorrectly simplified 4(1 + 3i), failing to distribute correctly.

Total Score Calculation

When combining complex scores, add real and imaginary parts separately.
Example: Melissa (5 - 4i) and Tomas (3 + 2i) have a total score of 8 - 2i.

Inverse Property of Addition

This property confirms that adding a number and its additive inverse results in zero.
Example: If x = a + bi and y = -a - bi, then x + y = 0.

Product of Complex Numbers

The product of two conjugate complex numbers can be calculated to yield a real number.
Example: (3 - 2i)(3 + 2i) results in 13.

Additive Identity Property

This property indicates that adding zero to a number does not change its value.
Example: (7 + 4i) + 0 equals 7 + 4i.

This quiz covers various operations with complex numbers, including their properties like additive inverses, associative and commutative properties, and their application in voltage calculations. Test your understanding through examples and explore common mistakes in the distributive property.