Operations with complex numbers

Front

What is the value of \( \sqrt{-4} \)?

Back

\( 2i \)

Front

What does \( i^2 \) equal?

Back

\( -1 \)

Front

Simplify the expression \( 2i - 7i + 10 \).

Back

\( -5i + 10 \)

Front

What is \( \sqrt{-28} \) simplified?

Back

\( 2i\sqrt{7} \)

Front

Simplify the expression \( 4i(-2 - 8i) \).

Back

\( 32 - 8i \)

Front

What is the definition of a complex number?

Back

A complex number is a number of 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 \( \sqrt{-1} \).

Front

How do you add complex numbers?

Back

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

Front

What is the conjugate of a complex number \( a + bi \)?

Back

The conjugate is \( a - bi \).

Front

How do you multiply complex numbers?

Back

To multiply complex numbers, use the distributive property and apply \( i^2 = -1 \) when necessary.