Imaginary Numbers

Front

What are 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

How do you simplify √-1?

Back

√-1 = i.

Front

What is the result of (a + bi)(c + di)?

Back

(a + bi)(c + di) = ac + adi + bci + bdi^2 = (ac - bd) + (ad + bc)i.

Front

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

Back

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

Front

How do you add complex numbers (a + bi) + (c + di)?

Back

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

Front

How do you subtract complex numbers (a + bi) - (c + di)?

Back

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

Front

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

Back

The modulus of a complex number a + bi is √(a² + b²).

Front

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

Back

The argument of a complex number a + bi is the angle θ in polar coordinates, given by θ = arctan(b/a).

Front

How do you multiply complex numbers (a + bi)(c + di)?

Back

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