Question 1

Which of the following is the correct result of $$ (7 + 4i) - (2 - 3i) $$ written in standard $$ a + bi $$ form?

Accepted Answer

$$ 5 + 7i $$

Question 2

Simplify $$ \sqrt{-8} $$ and write the answer in $$ a + bi $$ form.

Accepted Answer

$$ 2\sqrt{2}i $$

Question 3

If $$ z_1$ = 3 + 2i $$ and $$ z_2$ = 1 - 5i $$, what is $$ z_1$ \cdot z_2$ $$?

Accepted Answer

$$ 13 - 13i $$

Question 4

Which of the following is the solution to $$ x^2$ + 36 = 0 $$?

Accepted Answer

$$ x = 6i,\ x = -6i $$

Question 5

A medical imaging device uses the complex number $$ 5 - 8i  in $$its calculations. What is the modulus of this complex number?

Accepted Answer

$$ \sqrt{89} $$

Question 6

Which of the following is the conjugate of $$ -2 + 7i $$?

Accepted Answer

$$ -2 - 7i $$

Question 7

A chemical reaction is modeled by the quadratic equation $$ x^2$ - 4x + 13 = 0 . $$What are the roots?

Accepted Answer

$$ 2 + 3i,\ 2 - 3i $$

Question 8

Simplify $$ (5 + 2i)(3 - i) $$ and write the result in $$ a + bi $$ form.

Accepted Answer

$$ 17 + i $$

Question 9

A signal in an electrical circuit is represented by $$ z = 4 - 3i . $$What is the argument (angle) $$ 	heta  of$$ $$ z  in $$radians?

Accepted Answer

$$ \arctan\left(\frac{-3}{4}\right) $$

Question 10

Which of the following is the result of $$ \frac{7 + 4i}{2 - i}  in$$ $$ a + bi $$ form?

Accepted Answer

$$ 2 + 3i $$

Question 11

A quadratic equation $$ x^2$ + 2x + 5 = 0 $$ models the population growth of a species. What are the solutions?

Accepted Answer

$$ -1 + 2i,\ -1 - 2i $$

Question 12

If $$ z = 6i $$, what is $$ z^2$ $$?

Accepted Answer

$$ -36 $$

Question 13

A historical event is modeled by the equation $$ x^2$ - 9 = 0 . $$What are the solutions?

Accepted Answer

$$ x = 3,\ x = -3 $$

Question 14

Which of the following is the result of $$ (2 - 5i) + (4 + 3i) $$?

Accepted Answer

$$ 6 - 2i $$

Question 15

A quadratic equation $$ x^2$ + 4x + 8 = 0  is $$used in a physics experiment. What are the roots?

Accepted Answer

$$ -2 + 2i,\ -2 - 2i $$

Question 16

Simplify $$ (3 + 2i)^2$ $$ and write the result in $$ a + bi $$ form.

Accepted Answer

$$ 5 + 12i $$

Question 17

A population model uses the complex number $$ z = -4 + 3i . $$What is $$ |z| $$?

Accepted Answer

$$ 5 $$

Question 18

Which of the following is the result of $$ \sqrt{-36} $$?

Accepted Answer

$$ 6i $$

Question 19

A quadratic equation $$ x^2$ + 6x + 13 = 0  is $$used to model a chemical process. What are the roots?

Accepted Answer

$$ -3 + 2i,\ -3 - 2i $$

Complex Numbers and Quadratic Equations: Operations and Standard Forms

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