Complex numbers - practice problems - last page
Direction: Solve each problem carefully and show your solution in each item.Number of problems found: 57
- Quadratic 21643
Solve the quadratic equation: 2y²-8y + 12 = 0 - Linear imaginary equation
Given that 2(z+i)=i(z+i) "this is z star" Find the value of the complex number z. - Goniometric form
Determine the goniometric form of a complex number z = √ 110 +4 i. - The modulus
Find the modulus of the complex number 2 + 5i
- Distance two imaginary numbs
Find the distance between two complex numbers: z1=(-8+i) and z2=(-1+i). - Moivre 2
Find the cube roots of 125(cos 288° + i sin 288°). - Alternating circuit
In an alternating circuit, the total voltage V is given by V=V1 +V2 If V=(12.2+6.8i) V and V1=(7.8-2.5i) V, find the voltage V2. - Fifth 3871
What is the sum of the fifth root of 243? - Complex roots
Find the sum of the fourth square root of the number 16.
- Determine 3882
Determine the sum of the three square roots of 343. - ABS CN
Calculate the absolute value of the complex number -15-29i. - Stadium
A domed stadium is shaped like a spherical segment with a base radius of 150 m. The dome must contain a volume of 3500000 m³. Determine the dome's height at its center to the nearest tenth of a meter. - ABS, ARG, CONJ, RECIPROCAL
Let z=-√2-√2i where i2 = -1. Find |z|, arg(z), z* (where * indicates the complex conjugate), and (1/z). Where appropriate, write your answers in the form a + i b, where both a and b are real numbers. Indicate the positions of z, z*, and (1/z) on an Argand - Subtracting complex in polar
Given w =√2(cosine (pi/4) + i sine (pi/4) ) and z = 2 (cosine (pi/2) + i sine (pi/2) ). What is w - z expressed in polar form?
- De Moivre's formula There are two distinct complex numbers, such that z³ is equal to 1 and z is not equal to 1. Calculate the sum of these two numbers.
- Cis notation Evaluate the multiplication of two complex numbers in cis notation: (6 cis 120°)(4 cis 30°) Write the result in cis and Re-Im notation.
- Instantaneous 76754
For a dipole, calculate the complex apparent power S and the instantaneous value of the current i(t), given: R=10 Ω, C=100uF, f=50 Hz, u(t)= square root of 2, sin( ωt - 30 °). Thanks for any help or advice.
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