Complex Numbers

When solving a quadratic formula and the discriminant is 0, what type of solution will you get?

One real double root solution

When solving a quadratic equation and the discriminant is less than 0, what type of solution will you get?

Two complex solutions

Complex Number

a number of the form a+bi where a and b are real numbers and i is the square root of -1

Simplify (a-bi)(a-bi)

a^2-2abi-bi^2

Find the error. (16-3i)+(4+2i) 20-i^2 20-(-1) 20+1 21

i^2 is positive 1 not negative 1

What is the quadratic formula?

x = (-b ± √b^2 - 4ac)/2a (will get 2 answers)

Solve z^2 + 2z + 2 = 0

−1±i

Solve i(1+7i)−3i(4+2i)

−1−11i

Solve (1−3i)^3

−26 + 18i

simplify (6i)^3

-216

(- 2 - 4i) / i

-4 + 2i

Evaluate the following expression (3 + 2i) - (8 - 5i)

-5 + 7i

Simplify −1−8i−4−i

-5-9i

Evaluate the following expression (4 - 2i)(1 - 5i)

-6 - 22i

(- 3 + 2i) / (3 - 6i)

-7/15 - 4i/15

If (x + yi) / i = ( 7 + 9i ) , where x and y are real, what is the value of (x + yi)(x - yi)?

130

Rewrite the expression in standard form (2+3i)(1-4i)

2-5i-12i^2

Identify the imaginary number, 9+3i

3i

Solve (1+2i)(4−6i)^2

76 − 88i

Simplify 6(−7 + 6i)(−4 + 2i)

96 − 228i