# Complex numbers questions and answers Recent questions in Complex numbers
Complex numbers ### part of $10,000 is invested at 11% simple interest account, the rest is at 14% simple interest account. If the annual income is$1,265, how much is invested at each rate?

Complex numbers
ANSWERED ### Determine the absolute value of each of the following complex numbers: a. $$z = 5 + 12i$$ b. $$2 - 3i.$$

Complex numbers
ANSWERED ### Find the product of the complex numbers.Leave answers in polar form. $$\displaystyle{z}_{{1}}={1}+{i}$$ $$\displaystyle{z}_{{2}}=-{1}+{i}$$

Complex numbers
ANSWERED ### Write the complex number in trigonometric form $$r(\cos \theta + i \sin \theta)$$,with theta in the interval $$\displaystyle{\left[{0}^{\circ},{360}^{\circ}\right]}$$ $$\displaystyle{5}\sqrt{{3}}+{5}{i}$$

Complex numbers
ANSWERED ### Find the modulus of each of the complex numbers 5i, 7, and 3 + 4i.

Complex numbers
ANSWERED ### Find the real numbers x and y so that the equation is true. $$\displaystyle{x}−{2}{i}={7}+{y}{i}$$

Complex numbers
ANSWERED ### How to add complex numbers. Provide an example with your explanation.

Complex numbers
ANSWERED ### The exponential expression $$\displaystyle{2}^{{8}}$$ has a value of 256. Write two other exponential expressions that have a value of 256. Explain how you got your answers. (Begin by writing out $$\displaystyle{2}^{{8}}$$ as the product of 2s.)

Complex numbers
ANSWERED ### $$(−5)\times \cdots \times (−5) 17 times$$

Complex numbers
ANSWERED ### If z is a complex number, show that the sum of z and its conjugate is a real number.

Complex numbers
ANSWERED ### Write each complex number in standard form. $$2(\cos 30^{\circ} + i \sin 30^{\circ})$$

Complex numbers
ANSWERED ### In the example problem, $$\displaystyle{2.4}{x}{10}^{{6}}$$ was rewritten as $$\displaystyle{24}{x}{10}^{{5}}$$. Explain why those expressions are equivalent.

Complex numbers
ANSWERED ### Write standart form of complex number $$\displaystyle{5}{\left({{\cos{{135}}}^{\circ}+}{i}{\sin{{135}}}^{\circ}\right)}$$

Complex numbers
ANSWERED ### Use DeMoivre’s Theorem to find the indicated power of the complex number .Write answer in rectangular form. $$\displaystyle{\left(\sqrt{{3}}-{i}\right)}^{{6}}$$

Complex numbers
ANSWERED ### Write the complex number in standart form $$\displaystyle{6}{i}^{{2}}-{8}{i}^{{3}}$$

Complex numbers
ANSWERED ### Write the standard form of the complex number. $$\displaystyle{12}{\left({\cos{{\left({60}^{\circ}\right)}}}+{i}{\sin{{\left({60}^{\circ}\right)}}}\right)}$$

Complex numbers
ANSWERED ### Determine whether H is a subgroup of the complex numbers C with addition $$\displaystyle{H}={\left\lbrace{a}+{b}{i}{\mid}{a},{b}\in{R},{a}{b}\ge{0}\right\rbrace}$$

Complex numbers
ANSWERED ### Adam starts with the number z=1+2i on the complex plane. First, he dilates z by factor of 2 about the origin. Then, he reflects it across the real axis. Finally, he rotates it $$\displaystyle{90}^{\circ}$$ counterclockwise about the origin. The resulting complex number can be written in form a+bi where a and b are real numers. What is the resukring complex number?

Complex numbers
ANSWERED ### Solve by using De Moivre's Theorem (find real and imaginary part of complex number): $$\displaystyle{\left(\sqrt{{3}}+{i}\right)}^{{3}}$$
ANSWERED 