Complex Numbers

Front

What is a complex number?

Back

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit, defined as the square root of -1.

Front

What does the letter 'i' represent in complex numbers?

Back

The letter 'i' represents the imaginary unit, which is defined as the square root of -1.

Front

How do you add complex numbers?

Back

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

Front

How do you subtract complex numbers?

Back

To subtract complex numbers, subtract their real parts and their imaginary parts separately. For example, (a + bi) - (c + di) = (a - c) + (b - d)i.

Front

What is the product of (1-3i)(2+5i)?

Back

The product is 17 - i.

Front

What is the result of simplifying 3i - (4 + 7i)?

Back

The result is -4 - 4i.

Front

What is the sum of -6i and 3i?

Back

The sum is -3i.

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 multiply complex numbers?

Back

To multiply complex numbers, use the distributive property (FOIL method). For example, (a + bi)(c + di) = ac + adi + bci + bdi^2, and since i^2 = -1, combine like terms.

Front

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

Back

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