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 squared (i^2)?

Back

i^2 = -1.

Front

How do you simplify the expression √(-25)?

Back

√(-25) = 5i.

Front

What is the standard form of a complex number?

Back

The standard form of a complex number is a + bi, where a is the real part and b is the imaginary part.

Front

How do you multiply two complex numbers (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 two complex numbers?

Back

To add two complex numbers, add their real parts and their imaginary parts separately: (a + bi) + (c + di) = (a + c) + (b + d)i.

Front

How do you subtract two complex numbers?

Back

To subtract two complex numbers, subtract their real parts and their imaginary parts separately: (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 given by |a + bi| = √(a^2 + b^2).

Front

How do you divide two complex numbers?

Back

To divide two complex numbers, multiply the numerator and denominator by the conjugate of the denominator: (a + bi) / (c + di) = [(a + bi)(c - di)] / (c^2 + d^2).