# Complex numbers + square (second power, quadratic) - practice problems

#### Number of problems found: 16

- 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. - Difference 4102

Determine the difference between two complex numbers: 3i²-3i^{4}

- Determine 4083

Determine the sum of complex numbers: 2i² + 2i^{4} - Log

Calculate the value of expression log |-7 -i +i²| . - Eq2 equations

For each of the following problems, determine the roots of the equation. Given the roots, sketch the graph and explain how your sketch matches the roots given and the form of the equation: g(x)=36x²-12x+5 h(x)=x²-4x+20 f(x)=4x²-24x+45 p(x)=9x²-36x+40 g(x) - Equation: 3726

Determine the real root of the equation: x^-3: x^-8 = 32 - Quadratic 21643

Solve the quadratic equation: 2y²-8y + 12 = 0

- 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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