Complex Number Practice

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 i^2 = -1.

Front

What is the imaginary unit 'i'?

Back

Front

How do you multiply two complex numbers?

Back

To multiply two complex numbers (a + bi)(c + di), use the distributive property: ac + adi + bci + bdi^2, and simplify using i^2 = -1.

Front

What is the complex conjugate of a complex number?

Back

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

Front

What is the product of a complex number and its conjugate?

Back

The product of a complex number a + bi and its conjugate a - bi is a^2 + b^2.

Front

How do you add two complex numbers?

Back

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

Front

What is the result of multiplying (2i)(3i)?

Back

The result is -6, since (2i)(3i) = 6i^2 = 6(-1) = -6.

Front

What is the sum of (5 - 2i) + (-7 + 8i)?

Back

The sum is -2 + 6i.

Front

Simplify the expression (7 + 2i)(9 - 6i).

Back

The simplified expression is 75 - 24i.

Front

What is the complex conjugate of 4 - 3i?

Back

The complex conjugate is 4 + 3i.