The complex number z, where z = x + yi, can be graphed in the planeas 1x, y2. Describe the graphs of all complex numbers z satisfying the given conditions.63. The absolute value of z is 1. 64. The real and imaginary parts of z are equal.65. The real part of z is 1. 66. The imaginary part of z is 1.

Q: 4. Find the modulus, Iz], and argument, 0 , of the complex number. -1 + i

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Q: Find the intercepts and graph in the first octant the equation 4x + 8y = 16. If an intercept does…

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Q: 4. Recall the function p(x) = x? + 1. Write the zeros of the function The number i is a number such…

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Q: Find and graph all the roots in the complex plane. 3. (3+ 14)

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Q: Write the complex number in trigonometric form, once using degrees and once using radians. Begin by…

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Q: 2. The variables y, x > 0 are related by a formula of the form y = ax where a, b are fixed real…

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Q: 14. Solve for x. X4-9x² =0. * O A. {0, 2, -3} B. {0, -2, -3) C{0, 3, -3} D. {0, 3, -2)

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Q: 3.11. Let z1, 2,, Zn and w1, w2, , Wn be complex numbers. Estab- lish Lagrange's identity 2 ZkWk -…

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Q: Find and graph all roots in the complex plane. 25. Vi

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Q: 5. Graph the function and find the domain and range. 10 1 x + 6 x < -6 x +4 -6<x < 2 f(x) = 4 5 --x…

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Q: ure. 17 Solve for x. (4r+58)

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Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.