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mathematics
basic technical mathematics

Questions and Answers of Basic Technical Mathematics

Perform the indicated operations graphically. Check them algebraically.(7 + 4j) − (3j − 8)
Find the values of x and y for which the equations are valid.2xj − 2y = (y + 3)j − 3
Simplify each of the given expressions. 15 27 5
Represent each complex number graphically and give the rectangular form of each.2.50(cos 315.0° + j sin 315.0°)
Perform the indicated operations, expressing all answers in the form a + bj.j2√−7 −√−28 + 8j3
Express the given numbers in exponential form.5477j − 8573
Simplify each of the given expressions.(a) √−9√−16 (b) √(-9)(-16)
Perform the indicated operations graphically. Check them algebraically.(3 − j) + (6 + 5j)
Perform the indicated operations. Leave the result in polar form. (25/194°) (6/239°) (30/17°)(10/29°)
Find the values of x and y for which the equations are valid.3x − 2j = yj − 9
Represent each complex number graphically and give the rectangular form of each.160(cos 150.0° + j sin 150.0°)
Express the given numbers in exponential form.−634.6 − 528.2j
Perform the indicated operations, expressing all answers in the form a + bj.j√−7 − j6√112 + 3j
Perform the indicated operations, expressing all answers in simplest rectangular form. 2-(6-j) 1-2j
The power P (in W) supplied to a series combination of elements in an ac circuit is P = VI cos∅, where V is the effective voltage, I is the effective current, and ∅ is the phase angle between the
Simplify each of the given expressions.(a) (b) √−2√−8 √(-2)(-8)
Perform the indicated operations graphically. Check them algebraically.(−j − 2) − (−1 − 3j)
Perform the indicated operations. Leave the result in polar form. (4/24°) (10/326°) (1/62°) ³ (8/77°)
Represent each complex number graphically and give the rectangular form of each.6(cos 180° + j sin 180°)
Express the given numbers in exponential form.47.3 − 10.9j
Perform the indicated operations, expressing all answers in the form a + bj.(9 − 2j)(6 + j)
Perform the indicated operations, expressing all answers in simplest rectangular form. 5j-(3-j) 4 - 2j
A 220-V source with f = 60.0 Hz is connected in series to an inductance (L = 2.05 H) and a resistance R in an electric-motor circuit. Find R if the current is 0.250 A.
In Example 6, what should be the capacitance in order to receive a 680-kHz radio signal?Data from Example 6In the antenna circuit of a radio, the inductance is 4.20 mH, and the capacitance is
Perform the indicated operations graphically. Check them algebraically.(80 + 300j) − (260 + 150j)
Represent each complex number graphically and give the rectangular form of each.5.00(cos 54.0° + j sin 54.0°)
Perform the indicated operations. Leave the result in polar form. (6/137°) ² (2/141°)(6/195⁰)
Express the given numbers in exponential form.5.90 + 2.40j
Perform the indicated operations, expressing all answers in simplest rectangular form. 3+√-4 4-j
Perform the indicated operations, expressing all answers in the form a + bj.(2 − 3j)(5 + 4j)
Simplify each of the given expressions.(a) √(−15)2 (b) (√−15)2
Perform the indicated operations. Leave the result in polar form. (50/236°) (2/84°) 125/47°
Perform the indicated operations graphically. Check them algebraically.(−25 − 40j) − (20 − 55j)
Represent each complex number graphically and give the polar form of each.−2j
Express the given numbers in exponential form.100j + 600
Perform the indicated operations, expressing all answers in the form a + bj.√−6√−12√30
A capacitance (C = 95.2 nF) and an inductance are in series in the circuit of a receiver for navigation signals. Find the inductance if the frequency for resonance is 50.0 kHz.
Perform the indicated operations, expressing all answers in simplest rectangular form. 6-√-16 √-4
Simplify each of the given expressions.(a) (√−7)2 (b) √(−7)2
Perform the indicated operations graphically. Check them algebraically.(3 − 2j) − (4 − 6j)
Represent each complex number graphically and give the polar form of each.9j
Express the given numbers in exponential form.−30 + 20j
Perform the indicated operations, expressing all answers in simplest rectangular form. 48j 4 + 18j
Perform the indicated operations, expressing all answers in the form a + bj.(√−18√−4)(3j)
An inductance of 12.5 μH and a capacitance of 47.0 nF are in series in an amplifier circuit. Find the frequency for resonance.
Perform the indicated operations. Leave the result in polar form.(1∠142°)10
Express each number in terms of j.√−π4
Perform the indicated operations graphically. Check them algebraically.(−1 − 6j) + (3j + 6)
Express the given numbers in exponential form.−1 − 5j
Represent each complex number graphically and give the polar form of each.60
Perform the indicated operations, expressing all answers in the form a + bj.(8j − 5)(7 + 4j)
A resistor, an inductor, and a capacitor are connected in series across an ac voltage source. A voltmeter measures 12.0 mV, 15.5 mV, and 10.5 mV, respectively, when placed across each element
Perform the indicated operations, expressing all answers in simplest rectangular form. 3 7 - 6j
Perform the indicated operations. Leave the result in polar form.(2∠135°)8
Express each number in terms of j.−√−4π3
Perform the indicated operations graphically. Check them algebraically.(2 − 4j) + (j − 2)
Express the given numbers in exponential form.3 − 4j
Represent each complex number graphically and give the polar form of each.−3
Perform the indicated operations, expressing all answers in the form a + bj.(4 − j)(5 + 2j)
The reactance of an inductor is 1200Ω for f = 280 Hz. What is the inductance?
Perform the indicated operations. Leave the result in polar form.[3(cos120° + j sin120°)]4
Express each number in terms of j.−√−5/9
Perform the indicated operations graphically. Check them algebraically.(0.2 − 0.1j) − 0.1
Perform the indicated operations, expressing all answers in simplest rectangular form.(4 − 9j)(1 + 2j)
Express the given numbers in exponential form.82.76∠470.09°
Represent each complex number graphically and give the polar form of each.95.27j + 62.31
Perform the indicated operations, expressing all answers in the form a + bj.(−2.2 j)(1.5j − 4.0)
A resistance (R = 64.5Ω) and an inductance (L = 1.08 mH) are in a telephone circuit. If f = 8.53 kHz, find the impedance across the resistor and inductor.
Perform the indicated operations. Leave the result in polar form.[0.2(cos35° + j sin35°)]3
Perform the indicated operations. Leave the result in polar form. 2/90° 4/75°
Express each number in terms of j.−√−7/4
Perform the indicated operations graphically. Check them algebraically.5j − (1 − 4j)
Perform the indicated operations, expressing all answers in simplest rectangular form.(6 − 3j)(4 + 3j)
Express the given numbers in exponential form.9245∠296.32°
Represent each complex number graphically and give the polar form of each.3.514 − 7.256j
Perform the indicated operations, expressing all answers in the form a + bj.(7 − j)(7j)
A resistance (R = 25.3Ω) and a capacitance (C = 2.75 nF) are in an AM radio circuit. If f = 1200 kHz, find the impedance across the resistor and the capacitor.
Find the cube roots of j.
Express each number in terms of j.3√−48
Perform the indicated operations graphically. Check them algebraically.(3 − 2j) + (−1 − j)
Perform the indicated operations, expressing all answers in simplest rectangular form.−3j(4 − 7j)
Perform the indicated operations. Leave the result in polar form. 12/320° 5/-210°
Express the given numbers in exponential form.0.0192∠76.7°
Represent each complex number graphically and give the polar form of each.√2 − j√2
Perform the indicated operations, expressing all answers in the form a + bj.(0.062j − 0.073) − 0.030j − (0.121 − 0.051j)
Given that the voltage in a given circuit is 8.375 − 3.140j V and the impedance is 2.146 − 1.114 jΩ, find the magnitude of the current.
What is the capacitance of the circuit in a radio that has an inductance of 8.75 mH if it is to receive a station with frequency 600 kHz?
Express each number in terms of j.4√−8
Perform the indicated operations graphically. Check them algebraically.(5 − j) + (3 + 2j)
Perform the indicated operations, expressing all answers in simplest rectangular form.5 j(6 − 5j)
Perform the indicated operations. Leave the result in polar form. [3(cos115° + jsin115°)]² 45(cos80° + jsin 80°)
Represent each complex number graphically and give the polar form of each.1 + j√3
Express the given numbers in exponential form.4.06∠−61.4°
Perform the indicated operations, expressing all answers in the form a + bj.(12j − 21) − (15 − 18j) − 9j
Given that the current in a given circuit is 3.90 − 6.04 j mA and the impedance is 5.16 + 1.14 j kΩ, find the magnitude of the voltage.
Find the values of x and y: x + 2j − y = yj − 3xj.
Perform the indicated operations graphically. Check them algebraically.2j + (−2 + 3j)
Perform the indicated operations, expressing all answers in simplest rectangular form.(−4 − 2j) −√−49
Represent each complex number graphically and give the polar form of each.460 − 460j
Perform the indicated operations. Leave the result in polar form. 8(cos100° + jsin100°) 4(cos65°+ jsin 65°)

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