A complex valued function f(z) =z3−1−I, what is the solution of f (z) =0? Note: exp(z) = e^z

In: Advanced Math

What is the integral e^z/Z-1 dz where C is the circle|z| = 2?

In: Advanced Math

What are the coordinates of the image of the point (–3,6) after a dilation with a center of (0,0) and scale factor of 1/3 ?

In: Advanced Math

what are methods used to measure ingredients and their units of measure?

In: Advanced Math

Identify the average rate of change over the interval [-2,-1]

In: Advanced Math

The big jar of nickels and dimes contained $45. If 700 coins were in the jar, how many of each kind were there?

In: Advanced Math

solev tan^2 x =1 where x is more than or equal to 0 but x is less than or equal to pi

In: Advanced Math

In triangle PQR right-angled at Q , PQ = 3 cm and PR = 6 cm. Determine ∠QPR

In: Advanced Math

Two concentric circles are of radii 5 cm and 3 cm. Determine the length of the chord of the larger circle which touches the smaller circle.

In: Advanced Math

Sum of the areas of two squares is 468 m2. If the difference of their perimeters is 24 m, determine the sides of the two squares.

In: Advanced Math

Find the coordinates of the orthocenter of the triangle whose vertices are A(3, 1), B(0, 4) and C(-3, 1).

In: Advanced Math

Find y(0.5) for y′=-2x-y, x0=0,y0=-1, with step length 0.1 using Euler method (1st order derivative)

In: Advanced Math

Poducts z1 and z2 as a z1=5+3i and z2=4-2i, write the following in the form a+bi

In: Advanced Math

Find the Rank of a Matrix Using the Echelon Form of the above matrix.Give details step by step.

In: Advanced Math

Let \( B_1 = \left\{(2,1,1,1),(1,1,1,1),(1,1,2,1)\right\} \hspace{2mm} \)and \( \hspace{2mm}B_2 =\left\{(2,1,2,2)\right\}\hspace{2mm} \)be two subsets of\( \hspace{2mm} \mathbb{R}^4, E_1 \) be a subspace spanned by\( B_1, E_2 \)be a subspace spanned by \( B_2 \), and L be a linear operator on \( \mathbb{R}^4 \) defined by

\( L(v)=(-w +4x-y+z,-w+3x,-w+2x+y,-w+2x+z)\hspace{2mm},v=(w,x,y,z) \)

(a) Show that \( B_1 \) is a basis for \( E_1 \) and \( B_2 \) is a basis for \( E_2 \)

(b) Show that \( E_1 \) and \( E_2 \) are L-invariant. Find the matrices \( A_{1} =[L_{E_1}]_{B_1} \) and \( A_2=[L_{E_2}]_{B_2} \)

In: Advanced Math