# Algebra II: Complex numbers questions and answers Recent questions in Complex numbers
Complex numbers
ANSWERED ### What are the modulus and argument of the complex number z=a+bi?

Complex numbers
ANSWERED ### Plot each complex number in the complex plane: a. z = 2 + 3i b. z = -3 - 5i c. z = -4 d. z = -i.

Complex numbers
ANSWERED ### Plot the complex number. Then write the trigonometric form of the complex number. $$\displaystyle{5}−{5}{i}$$

Complex numbers
ANSWERED ### What is the complex plane? How do we graph a complex number z=a+bi in the complex plane?

Complex numbers
ANSWERED ### Plot the complex number. Then write the trigonometric form of the complex number. $$\displaystyle{1}−\sqrt{{{3}}}{i}$$

Complex numbers
ANSWERED ### Multiplicative Inverse of a Complex Number The multiplicative inverse of a complex number z is a complex number zm such that $$\displaystyle{z}\times{z}{m}={1}$$. Find the multiplicative inverse of complex number. $$\displaystyle{z}=−{2}+{8}{i}$$

Complex numbers
ANSWERED ### Plot the complex number. Then write thetrigonometric form of the complex number. $$\displaystyle{1}+{i}$$

Complex numbers
ANSWERED ### Multiplicative Inverse of a Complex Number The multiplicative inverse of a complex number z is a complex number zm such that $$\displaystyle{z}\times{z}{m}={1}$$. Find the multiplicative inverse of complex number. $$\displaystyle{z}={1}+{i}$$

Complex numbers
ANSWERED ### Multiplicative Inverse of a Complex Number The multiplicative inverse of a complex number z is a complex number zm such that $$\displaystyle{z}\times{z}{m}={1}$$. Find the multiplicative inverse of complex number. $$\displaystyle{z}={3}−{i}$$

Complex numbers
ANSWERED Complex numbers

### An $$8\times8$$ chessboard has a square cell (or box, like square a1) which measures $$\beta$$ inches on one side. Express the two possible moves of your knight in vector form with units in inches. What are the distances of each possible move from your original position in inches? What are their angles from the horizontal (x-axis)?

Complex numbers
ANSWERED ### The variable z is often used to denote a complex number and $$\bar{z}$$ is used to denote its conjugate. If $$z = a+bi,$$ simplify the expression $$\displaystyle{z}^{{{2}}}-\overline{{{z}}}^{{{2}}}$$

Complex numbers
ANSWERED ### Determine whether a linear, quadratic, or exponential function best models the data. Then, use regression to find the function that models the data.  $$\begin{array}{|c|c|}\hline x & 0 & 1 & 2 & 3 & 4 \\ \hline y & 100 & 89.5 & 78.9 & 68.4 & 57.8 \\ \hline \end{array}$$

Complex numbers
ANSWERED ### Explain the difference between the graphs of polynomial functions with a degree of 3 that have a positive leading coefficient and the graphs of those with a negative leading coefficient.

Complex numbers
ANSWERED ### One problem with all exponential growth models is that nothing can grow exponentially forever. Describe factors that might limit the size of a population.

Complex numbers
ANSWERED ### absolute value of a complex number, axis of symmetry, binomial, completing the square, complex conjugate, complex number, complex plane, discriminant, imaginary number, imaginary part, imaginary unit, maximum value, minimum value, parabola, quadratic function, quadratic inequality in two variables, quadratic model, quadratic regression, real part, root of an equation, standard form, trinomial, vertex form, vertex of a parabola, zero of a function. Complete the sentences below with vocabulary words from the list above. The number 5i can be classified as both a(n)_______ and a ______.

Complex numbers
ANSWERED ### Fill in the blanks. When evaluating limits at infinity for complicated rational functions, you can divide the numerator and denominator by the ____ term in the denominator.

Complex numbers
ANSWERED ### Complex number in rectangular form What is (1+2j) + (1+3j)? Your answer should contain three significant figures.

Complex numbers
ANSWERED ### Rhode Island is the smallest state in the United States. Its land area is about 2.9 x 10^10 square feet. Alaska, the largest state, is about 5.5 x 10^2 times as large as Rhode Island. What is the land are of Alaska in square feet? Write you answer in scientific notation.

Complex numbers
ANSWERED 