Reviewing Complex Numbers: Simplifying Expressions

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

How do you simplify the expression (3-5i)-(6+2i)?

Back

The simplified expression is -3-7i.

Front

What is the result of multiplying (6i^21)(-3i^51)?

Back

The result is -18.

Front

How do you simplify the expression (10+3i) - (2-9i)?

Back

The simplified expression is 8+12i.

Front

What is the value of i^86?

Back

The value is -1.

Front

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

Back

The product is 74.

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.

Front

How do you multiply two complex numbers?

Back

To multiply two complex numbers (a + bi)(c + di), use the distributive property and combine like terms: ac + adi + bci + bdi^2.