Complex numbers + square root - practice problems
Number of problems found: 13
- Cplx sixth power
Let z = 2 - sqrt(3i). Find z6 and express your answer in rectangular form. if z = 2 - 2sqrt(3 i) then r = |z| = sqrt(2 ^ 2 + (- 2sqrt(3)) ^ 2) = sqrt(16) = 4 and theta = tan -2√3/2=-π/3 - Subtract polar forms
Solve the following 5.2∠58° - 1.6∠-40° and give answer in polar form - Real roots
Determine the real root of the equation: x-3: x-8 = 32 - Modulus and argument
Find the mod z and argument z if z=i - Third roots
Determine the sum of the three complex third roots of the number 64 . - Root sum
What is the sum of the fifth root of 243? - Complex roots Find the sum of the fourth square root of the number 16.
- ABS CN
Calculate the absolute value of the complex number -6+19i. - Complex square roots
Determine the sum of the three square roots of 343. - 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.
- Dipole - complex power
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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