Complex Number Operations Review

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 is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as i = √(-1). It is used to represent the square root of negative numbers.

Front

What is the result of multiplying two complex conjugates, (a + bi)(a - bi)?

Back

The result is a^2 + b^2, which is a real number.

Front

What is the formula for adding two complex numbers?

Back

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

Front

What is the formula for subtracting two complex numbers?

Back

To subtract two complex numbers, (a + bi) and (c + di), you subtract the real parts and the imaginary parts separately: (a - c) + (b - d)i.

Front

What is the product of (7 - 5i)(7 + 5i)?

Back

The product is 74.

Front

What does i^2 equal?

Back

i^2 equals -1.

Front

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

Back

Use the distributive property: ac + adi + bci + bdi^2, which simplifies to (ac - bd) + (ad + bc)i.

Front

What is the result of multiplying 3i by (-2 + 4i)?

Back

The result is -12 - 6i.

Front

What is the geometric representation of complex numbers?

Back

Complex numbers can be represented on the complex plane, where the x-axis represents the real part and the y-axis represents the imaginary part.