4.1.7 Flashcard Review (Review B)

Front

What is the result of simplifying the expression (6 + 4i)(3 + 2i)?

Back

The result is 10 + 24i.

Front

How do you simplify the expression \frac{2 \pm \sqrt{80}}{4}?

Back

The simplified form is \frac{1 \pm 2 \sqrt{5}}{2}.

Front

What is the solution to the equation -x^2 - 14x - 8 = 4 in simplest form?

Back

The solutions are x = -7 \pm \sqrt{37}.

Front

How do you solve the equation 3x^2 + 8x - 5 = 10?

Back

The solutions are x = \frac{-4 \pm \sqrt{61}}{3}.

Front

What is the formula for multiplying two complex numbers?

Back

The formula is (a + bi)(c + di) = (ac - bd) + (ad + bc)i.

Front

What is the process for simplifying square roots in expressions?

Back

Factor the number under the square root into its prime factors and simplify by taking out pairs.

Front

What is the quadratic formula used for solving quadratic equations?

Back

The quadratic formula is x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.

Front

What does it mean for an expression to be in simplest form?

Back

An expression is in simplest form when it is fully simplified and cannot be reduced further.

Front

How do you combine like terms in complex numbers?

Back

Combine the real parts and the imaginary parts separately.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b^2 - 4ac) determines the nature of the roots: two real, one real, or two complex.