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mathematics
basic technical mathematics

Questions and Answers of Basic Technical Mathematics

Solve for x: 2x2 = 6x − 9 (Express the solutions in simplified form in terms of j.)
Determine the rectangular form and the polar form of the complex number for which the graphical representation is shown in the given figure. 36.0° 18.5 Imag. 0 Real
Solve for x: x2 = 8x − 41 (Express the solutions in simplified form in terms of j.)
Determine the rectangular form and the polar form of the complex number for which the graphical representation is shown in the given figure. Imag. 0 -24 7 ● Real
Determine the rectangular form and the polar form of the complex number for which the graphical representation is shown in the given figure. Imag. 40 Real
Evaluate 2x2 + 5x − 7 for x = −8 + 7j.
Evaluate x2 − 2x + 4 for x = 5 − 2j.
Explain why a real number is a complex number, but a complex number may not be a real number.
Show that the real part of x + yj equals the imaginary part of j(x + yj).
Find all the roots of the given equations.x5 − 32 j = 0
Is it possible that a given complex number and the negative of its conjugate are equal? Explain.
Find all the roots of the given equations.x4 + j = 0
Is it possible that a given complex number and its conjugate are equal? Explain.
Find all the roots of the given equations.x3 − 1 = 0
Change each number to polar form and then perform the indicated operations. Express the final result in rectangular and polar forms. Check by performing the same operation in rectangular form using a
What is the smallest positive value of n for which j−1 = jn?
Find all the roots of the given equations.x3 + 8 = 0
Evaluate j + j2 + j3 + j4 + j5 + j6 + j7 + j8.
Change each number to polar form and then perform the indicated operations. Express the final result in rectangular and polar forms. Check by performing the same operation in rectangular form using a
Evaluate: (a) j−8; (b) j−6
Change each number to polar form and then perform the indicated operations. Express the final result in rectangular and polar forms. Check by performing the same operation in rectangular form using a
How is a number changed if it is multiplied by (a) j4 ; (b) j2 ?
Perform the indicated operations. Leave the result in polar form.(536∠220.3°)4
Solve the given equations for x. Express the answer in simplified form in terms of j.3x2 − 6x + 4 = 0
Explain how to show that the reciprocal of the imaginary unit is the negative of the imaginary unit.
Perform the indicated operations. Leave the result in polar form.(7∠110.5°)3
Solve the given equations for x. Express the answer in simplified form in terms of j.x2 + 2x + 7 = 0
Perform the indicated operations. Leave the result in polar form.[3(cos36° + j sin36°)]6
Solve the given equations for x. Express the answer in simplified form in terms of j.x2 − 2x + 2 = 0
If the reciprocal of a + bj equals a − bj, what condition must a and b satisfy?
Perform the indicated operations. Leave the result in polar form.[2(cos16° + j sin16°)]10
Solve the given equations for x. Express the answer in simplified form in terms of j.x2 + 32 = 0
What type of number is the result of (a) Adding a complex number to its conjugate (b) Subtracting a complex number from its conjugate?
Perform the indicated operations. Leave the result in polar form.4.944∠327.49° + 8.009∠7.37°
Evaluate each expression on a calculator. Express answers in the form a + bj.(3j9 − 5j3)(4j6 − 6j8)
Change each number to polar form and then perform the indicated operations. Express the result in rectangular and polar forms. Check by performing the same operation in rectangular form.(−1 − j)3
Show the numbers a + bj, 3(a + bj), and −3(a + bj) on the same coordinate system. The multiplication of a complex number by a real number is called scalar multiplication of the complex number.3 −
Perform the indicated operations, expressing all answers in the form a + bj. j√2 - 5 j√2 + 3
Simplify each of the given expressions.−√(−j)2
Change each number to polar form and then perform the indicated operations. Express the result in rectangular and polar forms. Check by performing the same operation in rectangular form. 30 +
Represent each complex number graphically and give the rectangular form of each.0.9326∠229.54°
Give the polar and exponential forms of each of the complex numbers.−22 − 77j
Perform the indicated operations by using properties of exponents and express results in rectangular and polar forms.(4.55e1.32j)2
Perform the indicated operations, expressing all answers in the form a + bj. 12 + 10j 6-8j
Change each number to polar form and then perform the indicated operations. Express the result in rectangular and polar forms. Check by performing the same operation in rectangular form. 40j 2j+7
Show the given number, its negative, and its conjugate on the same coordinate system.5 − j
Simplify each of the given expressions.j48 + j200
Represent each complex number graphically and give the rectangular form of each.1.50∠897.7°
Give the polar and exponential forms of each of the complex numbers.4 − 3j3
Express the given complex numbers in polar and rectangular forms.820.7e−3.492j
Show the given number, its negative, and its conjugate on the same coordinate system.−3 − 5j
Perform the indicated operations, expressing all answers in the form a + bj. 1-j 3j
Simplify each of the given expressions.j15 − j13
Change each number to polar form and then perform the indicated operations. Express the result in rectangular and polar forms. Check by performing the same operation in rectangular form. 21 3 - 9j
Represent each complex number graphically and give the rectangular form of each.4.75∠172.8°
Give the polar and exponential forms of each of the complex numbers.1 − j
Express the given complex numbers in polar and rectangular forms.1724e2.391j
Show the given number, its negative, and its conjugate on the same coordinate system.4j − 2
Perform the indicated operations, expressing all answers in the form a + bj. 0.25 3-√-1
Simplify each of the given expressions.2j5 − 1/j−2
Perform the indicated operations graphically. Check them algebraically.(4j + 8) − (11 − 3j)
Represent each complex number graphically and give the rectangular form of each.cos 600.0° + j sin 600.0°
Express the given complex numbers in polar and rectangular forms.0.800e3.00j
Perform the indicated operations, expressing all answers in the form a + bj. 6j 2-5j
Change each number to polar form and then perform the indicated operations. Express the result in rectangular and polar forms. Check by performing the same operation in rectangular form.(1 + 5j)(4 +
Show the given number, its negative, and its conjugate on the same coordinate system.3 + 2j
Simplify each of the given expressions.j2 − j6
Perform the indicated operations graphically. Check them algebraically.(9 + 2j) − (5 − 6j)
Represent each complex number graphically and give the rectangular form of each.120(cos 270° + j sin 270°)
Express the given complex numbers in polar and rectangular forms.3.20e−5.41j
Change each number to polar form and then perform the indicated operations. Express the result in rectangular and polar forms. Check by performing the same operation in rectangular form.(7 − 3j)(8
Perform the indicated operations graphically. Check them algebraically.(6 − j) − 9 − (2j − 3)
Perform the indicated operations graphically. Check them algebraically.(7 − 2j) + (−5 + 4j)
Represent each complex number graphically and give the rectangular form of each.15(cos 0° + j sin 0°)
Express the given complex numbers in polar and rectangular forms.2.50e3.84j
Perform the indicated operations, expressing all answers in the form a + bj.(6 + 8j)(6 − 8j)
Change each number to polar form and then perform the indicated operations. Express the result in rectangular and polar forms. Check by performing the same operation in rectangular form.(5j −
Simplify each of the given expressions.(a) −j6 (b) (−j)6
Simplify each of the given expressions. -√(-3)(-7)√-21
Perform the indicated operations graphically. Check them algebraically.(2j + 1) − 3j − (j + 1)
Perform the indicated operations graphically. Check them algebraically.(−1 + 5j) + (4 + 6j)
Perform the indicated operations. Express results in polar form. See Example 3.307.5∠326.54° + 726.3∠96.41°Data from Example 3Perform the addition 1.563∠37.56° + 3.827∠146.23°. In order
Represent each complex number graphically and give the rectangular form of each.0.08(cos 360° + j sin 360°)
Express the given complex numbers in polar and rectangular forms.464e1.85j
Perform the indicated operations, expressing all answers in the form a + bj.(8 + 3j)(8 − 3j)
Change each number to polar form and then perform the indicated operations. Express the result in rectangular and polar forms. Check by performing the same operation in rectangular form.(3 + 4j)(5
Perform the indicated operations graphically. Check them algebraically.(−6 − 3j) + (2 − 7j)
Perform the indicated operations. Express results in polar form. See Example 3.7085∠115.62° − 4667∠296.34°Data from Example 3Perform the addition 1.563∠37.56° + 3.827∠146.23°. In order
Find the values of x and y for which the equations are valid.(x + jy)(7j − 4) = j(x − 5)
Represent each complex number graphically and give the rectangular form of each.220.8(cos 155.13° + j sin 155.13°)
Express the given complex numbers in polar and rectangular forms.20.0e1.00j
Perform the indicated operations, expressing all answers in the form a + bj.(8j + 20)2
(a) If the complex number j, in polar form, is multiplied by itself, what is the resulting number in polar and rectangular forms?(b) In the complex plane, where is the resulting complex number in
Simplify each of the given expressions.−√−5√−2√−10
Perform the indicated operations graphically. Check them algebraically.(3 − 6j) − (−1 − 8j)
Find the values of x and y for which the equations are valid.(3 + 2 j3)(x + jy) = 4 + j9
Express each expression in simplest form with only positive exponents. 9c-1 d-3
Use the circuit shown in Fig. 12.29. The current in the circuit is 5.75 mA. Determine the indicated quantities.The voltage across the inductor (between points b and c). a R = 2250 2 ww b XL = 1750
Express each of the given expressions in simplest form with only positive exponents. ax-² a-¹ + x-1 + a-²x
Represent each complex number graphically and give the rectangular form of each.3.00(cos 232.0° + j sin 232.0°)

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