Question

1. let $p = 5 - 2i$ and $q = -3 + 7i$. write each expression in the form $a + bi$.

a. $p + q$

b. $p - q$

Explanation:

Part a: \( p + q \)

Step1: Substitute \( p \) and \( q \)

Substitute \( p = 5 - 2i \) and \( q = -3 + 7i \) into \( p + q \), we get \( (5 - 2i) + (-3 + 7i) \).

Step2: Combine real and imaginary parts

Combine the real parts (\( 5 \) and \( -3 \)) and the imaginary parts (\( -2i \) and \( 7i \)) separately: \( (5 - 3) + (-2i + 7i) \).

Step3: Simplify

Simplify the real and imaginary parts: \( 2 + 5i \).

Step1: Substitute \( p \) and \( q \)

Substitute \( p = 5 - 2i \) and \( q = -3 + 7i \) into \( p - q \), we get \( (5 - 2i) - (-3 + 7i) \).

Step2: Distribute the negative sign

Distribute the negative sign to the terms inside the parentheses: \( 5 - 2i + 3 - 7i \).

Step3: Combine real and imaginary parts

Combine the real parts (\( 5 \) and \( 3 \)) and the imaginary parts (\( -2i \) and \( -7i \)) separately: \( (5 + 3) + (-2i - 7i) \).

Step4: Simplify

Simplify the real and imaginary parts: \( 8 - 9i \).

Answer:

\( 2 + 5i \)

Part b: \( p - q \)