Practice 5.4

Front

What is the result of the multiplication \( (3-i)(2+4i) \)?

Back

The result is \( 10 + 10i \).

Front

What is the conjugate of the complex number \( 5 + 7i \)?

Back

The conjugate is \( 5 - 7i \).

Front

What is the value of \( i^2 \)?

Back

The value is \( -1 \).

Front

What is the value of \( i^3 \)?

Back

The value is \( -i \).

Front

What is the square root of \( -1 \)?

Back

The square root is \( i \).

Front

What is the definition of 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 \( \sqrt{-1} \).

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 subtract two complex numbers?

Back

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

Front

What is the modulus of a complex number \( z = a + bi \)?

Back

The modulus is given by \( |z| = \sqrt{a^2 + b^2} \).