Math 2-Unit 3 Midterm Review Day 2

Front

What is a complex number?

Back

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit, defined as the square root of -1.

Front

How do you multiply two complex numbers?

Back

To multiply two complex numbers (a + bi) and (c + di), use the distributive property: (a + bi)(c + di) = ac + adi + bci + bdi^2. Remember that i^2 = -1.

Front

What is the result of multiplying (1 + 2i) and (3 + 4i)?

Back

-5 + 10i

Front

Evaluate (2 + 3i)(4 - 6i).

Back

26

Front

What is the result of multiplying (2 + 3i) and (5 - 2i)?

Back

16 + 11i

Front

What is a nonlinear system of equations?

Back

A nonlinear system of equations is a set of equations in which at least one equation is not linear, meaning it cannot be graphed as a straight line.

Front

How do you solve a nonlinear system of equations?

Back

To solve a nonlinear system, you can use substitution or elimination methods, or graph the equations to find their intersection points.

Front

What are the solutions to the system: y = x^2 + 10x + 16 and y = 3x + 4?

Back

(x, y) = (-3, -5) or (-4, -8)

Front

Evaluate (1 + 4i)(2 + 3i).

Back

-10 + 11i

Front

What is the conjugate of a complex number?

Back

The conjugate of a complex number a + bi is a - bi. It is used to simplify the division of complex numbers.