5(7+j2) Q1\ Simplify (2+ j5) +- 3- j4 - j(4- j6), expressing the result in the form x+jy.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 35E
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Q11 Simplify (2+ j5) + 2)- j(4 – j6), expressing the result in the form
3- j4
x + jy.
1
1
1
= -+ -
Q2\ If z, = 2+j, z, = -2+ j4 and
evaluate z, in the form
Z3
z, z,
x + jy and in polar form.
Q3\ If x and y are real, solve the equation:
= (2 + j}° – j4
X
y
%3D
2 -j 1+ j3
Q4\ If z and z are conjugate complex numbers, find two complex numbers,
z = z, and z = z, , that satisfy the equation 3zz+2(z-z)= 39+ j12.
Q5\ If z = x+ jy, where x and y are real, find the values of x and y when
3z
3z
+
4
%3D
1-j
j
3- j
Q6\ Solve the equation z +(-1+ j)z+j2 D0, giving the results in polar form.
Express the principal root in Cartesian coordinates.
2-j
in polar form. Express the principal root in
1+ j2
07| Find the three cube roots of
Cartesian coordinates.
Q8\ Determine the fifth roots of 2- j5 in polar coordinates.
Q9\ Solve the equation z +j2z+(1-j)=D0. Express the answer in exponential
and Cartesian forms.
Q10\ Express -2+j, 3+ j2, and 1- j2 in polar form and apply DeMoivre's
(1– j2)
(-2+ j)(3+j2)*
theorem to evaluate
Express the result in all forms.
Q11\ Express in the form x + jy
(1) etr/2-j)
(2) In(3– j)
(3) sin(at/4+ j2)
Q12\ Solve the equations:
1-j
1+j
; (2) In(z+ j)= ja/6 ; (3) z* = 4+ j3
(1) e
Transcribed Image Text:Problems Q11 Simplify (2+ j5) + 2)- j(4 – j6), expressing the result in the form 3- j4 x + jy. 1 1 1 = -+ - Q2\ If z, = 2+j, z, = -2+ j4 and evaluate z, in the form Z3 z, z, x + jy and in polar form. Q3\ If x and y are real, solve the equation: = (2 + j}° – j4 X y %3D 2 -j 1+ j3 Q4\ If z and z are conjugate complex numbers, find two complex numbers, z = z, and z = z, , that satisfy the equation 3zz+2(z-z)= 39+ j12. Q5\ If z = x+ jy, where x and y are real, find the values of x and y when 3z 3z + 4 %3D 1-j j 3- j Q6\ Solve the equation z +(-1+ j)z+j2 D0, giving the results in polar form. Express the principal root in Cartesian coordinates. 2-j in polar form. Express the principal root in 1+ j2 07| Find the three cube roots of Cartesian coordinates. Q8\ Determine the fifth roots of 2- j5 in polar coordinates. Q9\ Solve the equation z +j2z+(1-j)=D0. Express the answer in exponential and Cartesian forms. Q10\ Express -2+j, 3+ j2, and 1- j2 in polar form and apply DeMoivre's (1– j2) (-2+ j)(3+j2)* theorem to evaluate Express the result in all forms. Q11\ Express in the form x + jy (1) etr/2-j) (2) In(3– j) (3) sin(at/4+ j2) Q12\ Solve the equations: 1-j 1+j ; (2) In(z+ j)= ja/6 ; (3) z* = 4+ j3 (1) e
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