The variable z is often used to denote a complex number and z^- is used to denote its conjugate. If z = a+bi, simplify the expression

York 2021-09-30 Answered
The variable z is often used to denote a complex number and z¯ is used to denote its conjugate. If z = a+bi, simplify the expression
z2z2
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Anonym
Answered 2021-10-01 Author has 108 answers

With z=a+bi, the conjugate, z, is a-bi. Hence, the expression z2z2, is equivalent to
(a+bi)2(abi)2=[(a)2+2(a)(bi)2][(a)22(a)(bi)+(bi)2]
(use(a+b)2=(a)2+2(a)(b)+(b)2)
=[a2+2abi+b2i2][a22abi+b2i2]=a2+2abi+b2i2a2+2abib2i2=(a2a2)+(2abi+2abi)+(b2i2b2i2)=0+4abi+0=(4abi)i.
Hence, z2z2=(4abi)i.

Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2020-12-17
To calculate:The score Lily must earn on her fifth test to have an overage of 80 if on Lily's four College Algebra tests, her scores were 71,79,83 and 89.
asked 2021-01-22
Find the x- and y-intercepts of the graph of the equation.
y=14x6
asked 2021-09-24
Involve rational functions that model the given situations. In each case, find the horizontal asymptote as x and then describe what this means in practical terms.
f(x)=150x+1200.05x+1 the number of bass. f(x), months in a lake that was stocked with 120 bass.
asked 2021-09-28
Substitution and elimination, and matrix methods such as the Gauss-Jordan method and Cramers
asked 2021-02-05

To calculate:To check if (fg)(x)=(gf)(x). Professor Harsh gave a test to his college algebra class and nobody got more than 80 points (out of 100) on the test. One problem worth 8 points had insufficient data, so nobody could solve that problem.
The professor adjusted the grades for the class by
a. Increasing everyone's score by 10% and
b. Giving everyone 8 bonus points
c. x represents the original score of a student

asked 2021-06-10
Eastside Golden Eagles scored 60 points on a combination of two-polnt shots and three-point shots. If they made a total of 27 shots. how many of each kind of shot was made ?
asked 2020-10-18
To calculate:
The points needed on the final to avetage the points to 75.
Given information:
Grades in three tests in College Algebra are 87, 59 and 73.
The average after final is 75.