Imaginary Numbers and Operations

Front

Define imaginary numbers.

Back

Imaginary numbers are numbers that can be written as a real number multiplied by the imaginary unit 'i', where i is defined as the square root of -1.

Front

What is the value of i^2?

Back

i^2 = -1.

Front

Simplify √-1.

Back

√-1 = i.

Front

What is the result of adding two imaginary numbers, (a + bi) + (c + di)?

Back

(a + c) + (b + d)i.

Front

What is the result of multiplying two imaginary numbers, (a + bi)(c + di)?

Back

(ac - bd) + (ad + bc)i.

Front

Simplify √-4.

Back

√-4 = 2i.

Front

Calculate (5-2i) + (-7+8i).

Back

(5-2i) + (-7+8i) = -2 + 6i.

Front

Calculate (2i)(3i).

Back

(2i)(3i) = 6i^2 = -6.

Front

Calculate (3i)(-2+4i).

Back

(3i)(-2+4i) = -6i + 12i^2 = -12 - 6i.

Front

Multiply: (4 – 3i)(-7 – 2i).

Back

(4 – 3i)(-7 – 2i) = -28 - 8i + 21i + 6 = -34 + 13i.