Remote Day Units 1-6 Review

Front

Simplify: (2 - 3i)(5 + 4i)

Back

22 - 7i

Front

What is the formula for the magnitude of a vector r = (x, y)?

Back

|r| = √(x² + y²)

Front

Simplify: (3 + 2i) + (4i + 6)

Back

9 + 6i

Front

What is cot(x) in terms of sine and cosine?

Back

cot(x) = cos(x) / sin(x)

Front

What is the definition of a complex number?

Back

A complex number is a number of the form a + bi, where a and b are real numbers and i is the imaginary unit.

Front

What is the imaginary unit i?

Back

i is defined as the square root of -1.

Front

What is the formula for the sum of two complex numbers?

Back

(a + bi) + (c + di) = (a + c) + (b + d)i

Front

What is the product of two complex numbers (a + bi)(c + di)?

Back

(a + bi)(c + di) = (ac - bd) + (ad + bc)i

Front

What is the definition of a vector?

Back

A vector is a quantity that has both magnitude and direction.

Front

How do you find the resultant vector of two vectors?

Back

Use the Pythagorean theorem: |r| = √(x² + y²) for perpendicular vectors.