# Complex numbers + square root - practice problems

#### Number of problems found: 11

- Let z 2

Let z = 2 - sqrt(3i). Find z^{6}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 - Determine 3888

Determine the sum of the three-third roots of the number 64. - Equation: 3726

Determine the real root of the equation: x^-3: x^-8 = 32

- 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, 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. - 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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