Practice Problems and Examples for Complex Numbers

How do you simplify $2 (\cos (\frac{π}{2}) i \sin (\frac{π}{2}) \cdot 2 (\cos (\frac{3 π}{2}) + i \sin (\frac{3 π}{2}))$ and express the result in rectangular form?

GrareeCowui 2022-01-29

How do you simplify $6 [\cos (- \frac{π}{3}) + i \sin (- \frac{π}{3}) \cdot 3 (\cos (\frac{5 π}{6}) + i \sin (\frac{5 π}{6}))$ and express the result in rectangular form?

Duncan Reed 2022-01-29

How do I find the trigonometric form of the complex number $3 - 3 \sqrt{3} i$ .

Selena Cowan 2022-01-29

How do you write the trigonometric form of $- 1 + \sqrt{3} i$ ?

Kamren Franco 2022-01-29

How do you express the complex number in rectangular form: $12 ({\cos 60}^{\circ} + i {\sin 60}^{\circ})$ ?

Cassarrim1 2022-01-29

How do you express the complex number in rectangular form: $z = 5 ({\cos 120}^{\circ} + i {\sin 120}^{\circ})$ ?

Mary Buchanan 2022-01-18

How can we find z when the complex number Z satisfies the equation $4 z 3 \overset{―}{z} = (\frac{1 - 8 i}{2 - i})$ ,where $\overset{―}{z}$ is the complex conjugate of z?

kerrum75 2022-01-18

Find the quotient $\frac{z_{1}}{z_{2}}$ of the complex numbers.Leave answers in polar form.Express the argument as an angle between $0^{\circ}$ and $360^{\circ}$ .
$z_{1} = {\cos 70}^{\circ} + i {\sin 70}^{\circ}$
$z_{2} = {\cos 230}^{\circ} + i {\sin 230}^{\circ}$

agreseza 2022-01-18

Determine whether the statement When I add or subtract complex numbers, I am basically combining like terms., makes sense or does not make sense, and explain your reasoning.

Bobbie Comstock 2022-01-18

What is the largest integer $n < 0$ so that ${(\frac{1 + \sqrt{3}}{3} i)}^{n}$ is purely imaginary?

Danelle Albright 2022-01-18

How do you simplify ${(- i)}^{3}$ ?

Joyce Smith 2022-01-18

If $\frac{z - 1}{z + 1}$ is purely an imaginary number and is not equal to -1, then what is the value of the modulus of z?

Pamela Meyer 2022-01-18

Is there any example of a real world phenomenon modelled as $x^{2} + 1 = 0$ , (or even a cubic equation) based on which Complex numbers were invented? What is the physical quantity which is square of itself and when added with 1 can become zero.

Carol Valentine 2022-01-18

If x and y are real what is the complex conjugate z when: $ \frac{x + i y + 1}{x + i y}$ ? I tried to tidy up the $\frac{1}{x + i y}$ to get $\frac{x - i y}{x^{2} - y^{2}}$ , multiply it out etc but still just no cigar.

kihanja20 2022-01-18

What is the complex function of $f (z) = \frac{1}{z}$ ?

kihanja20 2022-01-18

What is the sum of this imaginary number series problem:
$i + 2 i^{2} + 3 i^{3} + 4 i^{4} + 5 i^{5} + \dots + 2002 i^{2002}$ ?

Jean Blumer 2022-01-18

How do you simplify $- 9 - 9 i \div - 1 - 8 i$ ?

Brock Brown 2022-01-18

How do you divide $\frac{- 2 - 5 i}{3 i}$ ?

sputneyoh 2022-01-18

How do you simplify $\frac{7 i}{8 + i}$ ?

Joan Thompson 2022-01-18

How do I find the complex conjugate of $\frac{12}{5 i}$ ?

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

Understanding Complex Numbers - Examples and Equations