Complex numbers Questions and Answers

Find the complex zeros of the following polynomial function. Write f in factored form. f(x)=x³ +27 The complex zeros of f are Use the complex zeros to factor f f(x) =

Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form.

Find Z₁ Z₂, and if z₁ = 2( cos 45° + i sin 45°) and Z₂ = 4( cos 25° + i sin 25°). Write your answers in standard polar form with the argument in degrees.

Find zw and Write each answer in polar form and in exponential form. The product zw in polar form is and in exponential form is

Write the following complex number in trigonometric form. Write the magnitude in exact form. Write the argument in radians and round it to two decimal places if necessary. 5-8i

Solve the cubic equation. x³ +729=0

Write the following complex number in trigonometric form. Write the magnitude in exact form. Write the argument in radians and round it to two decimal places if necessary. -2-3i

Write the following complex number in standard form, z = a + bi. Write the exact answer. Do not round. 5 (cos (11π/6) + isin (11π/6))

Use DeMoivre's Theorem to calculate the following expression. Express your answer in the form found using Euler's Formula. |z|n ein0 [3 (cos(240°) + isin (240°))]8

Write the following complex number in standard form, z = a + bi. Use the exact form if possible; otherwise, use a decimal approximation rounded to the hundredths place. 5 (cos(315°) + isin (315°))

Perform the following multiplication and write the product in trigonometric form. Express your result in the exact form, if possible; otherwise, use a decimal approximation rounded to the nearest hundredth. [4(cos(5π/4)+ isin (5π/4)][(4cos(3π/2)+isin(3π/2))] Solve the problem above and enter your solution below in trigonometric form. Recall that answers entered in degrees will require a degree symbol, which is located in the keypad.

Perform the following division and write the quotient in trigonometric form. Write the magnitude in exact form. Write the argument in radians and round it to two decimal places if necessary. -6i/ 2+i

Perform the following multiplication and write the product in standard form. Express your result in the exact form, if possible; otherwise, use a decimal approximation rounded to the nearest hundredth. (-1-3i)(-2+3i)

Write the following complex number in trigonometric form. Write the argument in radians, and if possible, use the exact form. Otherwise, use a decimal approximation rounded to the hundredths place. -4-2i

Evaluate the series. 4Σ (i+1) i=1 i=14Σ (i+1) = (Simplify your answer. Type an integer or a simplified fraction.)

Write the expression in rectangular form, x + yi, and in exponential form, r eiθ (1-i)5 The rectangular form of the given expression is __, and the exponential form of the given expression is __ (Simplify your answers. Type exact answers, using t as needed. Use integers or fractions for any numbers i