Write the expression in rectangular form, \( x+y i \), and in exponential form, re \( \left[6\left(\cos \frac{3 \pi}{10}+i \sin \frac{3 \pi}{10}\right)\right]^{5} \) The rectangular form of the given expression is \( \square \), and the exponential form of the given expression is (Simplify your answers. Type exact answers, using \( \pi \) as needed. Use integers or fractions for any numbers in the expressions.)

Find the direction angle of \( v \) for the following vector. \( v=2 i-4 j \) What is the direction angle of \( v \) ? TRound to one decimal place as needed.)

Determine la forma polar del complejo \( z=-3-\sqrt{3} i \)

Find \( \|\mathbf{v}\| \). \( \begin{array}{l}\mathbf{v}=9 \mathbf{i}-12 \mathbf{j} \\ \|\mathbf{v}\|=\square \text { (Type an exact answer, using radicals as needed. Simplify your answer.) }\end{array} \)

Write the vector v in the form \( \mathrm{ai}+\mathrm{bj} \), given its magnitude \( \|\mathrm{v}\| \) and the angle \( \alpha \) it makes with the positive \( x \)-axis, \[ \alpha v=45^{\circ} \] \( \mathrm{v}=\square \) (Simplify your answer. Type an exact answer using radicals as needed. Type your answer in the form ai + bj.)

Постройте график функции и укажите для нее область определения и значения \( x \), при которых \( y>0 \). а) \( у=3 \mathrm{x}^{-3} \);