Math

what are the indicated powers of these complex numbers:
a. (2 – 3i )^2
b. (3 + 4i )^3
c. [2 cis(300°)]^5
d. ( cos (4pi/3) + i sin (4pi/3)) ^4

  1. 👍
  2. 👎
  3. 👁
  1. a. just square it
    (2 - 3i)^2
    = 4 - 12i + 9i^2
    = 4 - 12i - 9
    = -5 - 12i

    De Moivre's theorem for the others, I will do c.

    c. [2 cis(300°)]^5
    = 2^5 cis 1500° , dividing out multiples of 360, keeping the remaining angle
    = 32cis60°
    or 32(cos60 + i sin60)
    = 32(√3/2 + i (1/2) )
    = 16√3 + 16i

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. American government

    What are powers of the U.S. government that are named and listed in the Constitution called? A.expressed powers B.implied powers C.inherent powers D.prohibited powers

  2. Government

    What are the reserved powers outlined in the tenth amendment? powers that are not delegated to the federal government and therefore granted to the states, as long as they are not prohibited by the Constitution. powers granted to

  3. Precalc

    To which set(s) of numbers does the number sqrt -16 belong? Select all that apply. real numbers complex numbers*** rational numbers imaginary numbers*** irrational numbers I can only pick two, and that's what I think it is. Please

  4. American Government

    the power of congress to print money is one of the legislative? A.Implied powers B.Expressed powers C.Inherent powers D.Nonlegislative powers

  1. civics

    Which of the following are powers that are exercised by both the national government and state governments at the same time? A.concurrent powers B. enumerated powers C. prohibited powers D. reserved powers

  2. English

    Identify the structure used in each of the sentences below. 1. The hamburger came from Hamburg, Germany, and the hot dog came from Frankfurt. simple compound complex compound-complex 2. The idea of placing meat on a bun, however,

  3. civics

    The phrase, “the Elastic Clause,” comes from which powers of Congress? A.enumerated powers***** B.implied powers C.inherent powers D.reserved powers Please help asap

  4. Civivs

    The phrase, "the Elastic Clause," comes from which power of Congress?? A.) Enumerated Powers B.) Implied Powers C.) Inherent Powers D.) Reserved Powers This is Unit 2, Lesson 14: Unit Test: Three Branches of Government

  1. check my work

    1. Which of the following provides the best definition of a strict constructionist interpretation of congressional power? (1 point) Congress must have more powers than the states. Congress should only use implied powers when

  2. Math

    How many numbers between 100 and 200 can be expressed as powers of 2??

  3. Civics

    How do the powers of the national government and the powers of the states compare, according to James Madison, the primary author of the Constitution? A.The powers of the national government are few, while the powers of the states

  4. Government

    Homework Help Powers that are shared by both the National Government and the States are called... A) reserved powers B) enumerated powers C) inherent powers D) implied powers E) concurrent powers The Supreme Court carries out most

You can view more similar questions or ask a new question.