Practice Problems and Examples for Complex Numbers

Find all complex numbers satisfying
$| z + 3 + 4 i | = | z - 5 |$

diferira7c 2022-01-15

Write the complex number $\frac{- 5 - 3 i}{4 i}$ in standard form?

Mary Keefe 2022-01-15

Multiply and simplify the following complex numbers:
$(- 3 - 2 i) \times (- 4 + 2 i)$

Joyce Smith 2022-01-15

Multiply each complex number by its complex conjugate.
a) $3 + 6 i$
b) $2 - 5 i$

Donald Johnson 2022-01-15

Factor the expressions over the set of complex numbers. For assistance, consider these examples
In Section R.3 we saw that some expressions factor over the set of integers. For example: $x^{2} - 4 = (x + 2) (x - 2)$
Some expressions factor over the set of irrational numbers. For example: $x^{2} - 5 = (x + \sqrt{5}) (x - \sqrt{5})$
To factor an expression such as $x^{2} + 4$ , we need to factor over the set of complex numbers. For example, verify that $x^{2} + 4 = (x + 2 i) (x - 2 i)$
a) $x^{2} - 9, x^{2} + 9$
b) $x^{2} - 100, x^{2} + 100$
c) $x^{2} - 64, x^{2} + 64$

reproacht3 2022-01-15

Plot the complex numbers 5i and $- 8 + 7 i$ in the complex plane.

Joanna Benson 2022-01-15

How do I solve $a r g (\frac{z - i}{z + i}) = \frac{π}{4}$ ?

garnentas3m 2022-01-15

How do you divide $\frac{3 + 9 i}{- 6 - 6 i}$ ?

Carla Murphy 2022-01-15

How do you write the complex conjugate of the complex number $\sqrt{- 15}$ ?

b2sonicxh 2022-01-15

How do you simplify $5 i \cdot i$ ?

Kathleen Rausch 2021-12-31

Complex arithmetic with conjugates Show that the conjugate of the sum (product, or quotient) of two complex numbers, $z_{1}$ and $z_{2}$ , is the same as the sum (product, or quotient) of their conjugates.

Stefan Hendricks 2021-12-30

Explain how to multiply complex numbers and give an example.
$3 + 2 i$ and $2 - 3 i$

regatamin2 2021-12-30

Explain how to add complex numbers.
$5 + 2 i$
$8 + 7 i$

Sapewa 2021-12-28

Having the following complex numbers $A = 5 - 2 i$ and $B = 3 + 8 i$
a) $A + B$
b) $B - A$
c) $A \times B$
d) What is the complex conjugate of A and the complex conjugate of B?
e) $\frac{B}{A}$ (B divide by A)

kloseyq 2021-12-26

Find the sum and the product of the complex numbers $3 - 2 i$ and $- 3 + 5 i$ .

feminizmiki 2021-12-20

Find the product of the complex numbers $z_{1} = \cos \frac{π}{6} + i \sin \frac{π}{6}$ and $z_{2} = \cos \frac{π}{4} + i \sin \frac{π}{4}$
Leave answer in polar form.

veksetz 2021-12-18

Find the product of the complex numbers
$z_{1} = 6 ({\cos 20}^{\circ} + i {\sin 20}^{\circ})$ and $z_{2} = 5 ({\cos 50}^{\circ} + i {\sin 50}^{\circ})$ . Leave answers in polar form.

quiquenobi2v6 2021-12-14

Choose a number X at random from the set of numbers ${1, 2, 3, 4, 5}$ . Now choose a number at random from the subset no larger than X, that is, from ${1, \dots, X}$ . Call this second number Y.
a) Find the joint mass function of X and Y.
b) Find the conditional mass function of X given that Y=i. Do it for i=1, 2, 3, 4, 5.
с) Are X and Y independent? Why?

Mary Hammonds 2021-12-13

Regardless if you’re dealing with complex numbers problems or need to find the answers to the complex numbers equation, do not let it bring you down as we shall provide you with complex numbers examples that will help you find the answers. Our complex numbers problems will offer you various solutions that can be matched to your instructions and the problems that you have. It is recommended to start with the complex numbers answers by going straight to your instructions to understand how exactly complex numbers differ. Have a look at our complex numbers questions and come up with solutions.

Precalculus