1. Equations & Inequalities

Find the sum. Express your answer in standard form. $5\left(4+7i\right)+6\left(3-2i\right)$

Perform the indicated operation. Express your answer in standard form. $\left(3+8i\right)^2$

Find the product. Express your answer in standard form. $2i\left(9-4i\right)\left(6+5i\right)$

Find the product of the given complex number and its conjugate. $4-5i$

Find the product of the given complex number and its conjugate. $-7-i$

Find the quotient. Express your answer in standard form.  

$\frac{6+i}{4-2i}$

Find the quotient. Express your answer in standard form. 

$\frac{-5+3i}{-7-4i}$

Decide whether each statement is true or false. If false, correct the right side of the equation. √-25 = 5i

Decide whether each statement is true or false. If false, correct the right side of the equation. i¹² = 1

Decide whether each statement is true or false. If false, correct the right side of the equation. (-2+7i) - (10-6i)= -12+i

Identify each number as real, complex, pure imaginary, or nonreal com-plex. (More than one of these descriptions will apply.) √24

Identify each number as real, complex, pure imaginary, or nonreal com-plex. (More than one of these descriptions will apply.) √-36

Write each number as the product of a real number and i. √-25

Perform each operation. Write answers in standard form. 15i- (3+2i) -11

Perform each operation. Write answers in standard form. (-8+2i)(-1+i)