Imaginary Numbers

Front

What is an imaginary number?

Back

An imaginary number is a complex number 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

How do you simplify the expression i^n for n = 31?

Back

To simplify i^31, divide 31 by 4. The remainder is 3, so i^31 = i^3 = -i.

Front

What is the result of multiplying (4 – 3i) and (-7 – 2i)?

Back

The result is -34 + 13i.

Front

What is the square root of -1?

Back

The square root of -1 is i.

Front

How do you simplify √-4?

Back

√-4 = √(4) * √(-1) = 2i.

Front

What is the value of i^4?

Back

i^4 = 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 express a complex number in standard form?

Back

A complex number is expressed in standard form as a + bi, where a is the real part and b is the imaginary part.

Front

What is the conjugate of a complex number a + bi?

Back

The conjugate of a complex number a + bi is a - bi.