Module 3 Study Guide

Front

What is the result of the operation \( (9+3i) - (-2-7i) \) in standard form?

Back

The result is \( 11 + 10i \).

Front

How do you simplify \( \frac{8}{6-2i} \) to standard form?

Back

The simplified form is \( \frac{6+2i}{5} \).

Front

What is the product of \( (5+6i)(-4+7i) \)?

Back

The product is \( -62 + 11i \).

Front

Evaluate the expression \( -\sqrt{-36} \).

Back

The evaluation gives \( -6i \).

Front

When graphing an inequality, which symbols require a dotted line?

Back

The symbols < and > require a dotted line.

Front

What is the standard form of a complex number?

Back

A complex number is in standard form if it is expressed as \( a + bi \), where \( a \) and \( b \) are real numbers.

Front

How do you add two complex numbers?

Back

To add two 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 two complex numbers?

Back

To multiply, use the distributive property and combine like terms, remembering that \( i^2 = -1 \).

Front

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

Back

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