Complex Number Operations

Front

What is the square of the complex number (2 + 3i)?

Back

(2 + 3i)² = -5 + 12i.

Front

What is the value of i²?

Back

i² = -1.

Front

What is the product of the complex numbers (3 - 2i) and (7 + 6i)?

Back

(3 - 2i)(7 + 6i) = 33 + 4i.

Front

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

Back

(5 - 2i) + (-7 + 8i) = -2 + 6i.

Front

Simplify the expression i√-2 * i√-8.

Back

i√-2 * i√-8 = 4.

Front

Define 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.

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as the square root of -1.

Front

How do you add two complex numbers?

Back

To add two complex numbers, add their real parts and their imaginary parts separately.

Front

How do you multiply two complex numbers?

Back

To multiply two complex numbers, use the distributive property (FOIL) and combine like terms.

Front

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

Back

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