Imaginary Numbers

Front

What is the value of √-1?

Back

i

Front

How do you multiply complex numbers (3i)(-2+4i)?

Back

-12-6i

Front

What is the value of i^6?

Back

-1

Front

What is the value of i^{89}?

Back

i

Front

How do you add complex numbers (5-2i) + (-7+8i)?

Back

-2+6i

Front

What is the definition of an imaginary number?

Back

An imaginary number is a number that can be written as a real number multiplied by the imaginary unit i, where i is defined as √-1.

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as the square root of -1.

Front

What is the pattern in the powers of i?

Back

The powers of i cycle every four: i^1 = i, i^2 = -1, i^3 = -i, i^4 = 1.

Front

How do you simplify i^n for any integer n?

Back

To simplify i^n, divide n by 4 and use the remainder to determine the equivalent power of i.

Front

What is the result of (a + bi)(c + di) where a, b, c, d are real numbers?

Back

The result is (ac - bd) + (ad + bc)i.