1. Equations & Inequalities

In Exercises 1–8, add or subtract as indicated and write the result in standard form. 8i - (14 - 9i)

Identify each number as real, complex, pure imaginary, or nonreal com-plex. (More than one of these descriptions will apply.) 0

In Exercises 9–20, find each product and write the result in standard form. (2 + 3i)^2

Write each number as the product of a real number and i. √-10

In Exercises 21–28, divide and express the result in standard form. - 6i/(3 + 2i)

Perform each operation. Write answers in standard form. -5i(3-i)²

Find each product or quotient. Simplify the answers. √-24 / √8

In Exercises 37–52, perform the indicated operations and write the result in standard form. √-64 - √-25

Find each sum or difference. Write answers in standard form. (3+2i) + (9+3i)

In Exercises 37–52, perform the indicated operations and write the result in standard form. √-8 (√-3 - √5)

In Exercises 48–57, perform the indicated operations and write the result in standard form. (7-i)(2+3i)

Find each product. Write answers in standard form. (2+i)(3-2i)

In Exercises 61–64, write each complex number in standard form. (1 + i)^3

Find each product. Write answers in standard form. i(3-4i)(3+4i)

In Exercises 65–70, perform the indicated operation(s) and write the result in standard form. (4 - i)^2 - (1 + 2i)^2

Find each quotient. Write answers in standard form. -5 / i

Simplify each power of i. i^23

In Exercises 95–99, perform the indicated operations and write the result in standard form. 8/(1 + 2/i)

Work each problem. Show that √2/2 + √2/2 i is a square root of i.