91Ó°ÊÓ

Find the magnitude of the vector a and the smallest positive angle \(\boldsymbol{\theta}\) from the positive \(\boldsymbol{x}\) -axis to the vector \(O P\) that corresponds to a. $$\mathbf{a}=\langle- 2,-2 \sqrt{3}\rangle$$

Use Euler's formula to prove De Moivre's theorem.

Express the complex number in trigonometric form with \(0 \leq \theta<2 \pi\) $$-7$$

Find the magnitude of the vector a and the smallest positive angle \(\boldsymbol{\theta}\) from the positive \(\boldsymbol{x}\) -axis to the vector \(O P\) that corresponds to a. $$\mathbf{a}=-4 \mathbf{i}+5 \mathbf{j}$$

Express the complex number in trigonometric form with \(0 \leq \theta<2 \pi\) $$-5$$

Find the magnitude of the vector a and the smallest positive angle \(\boldsymbol{\theta}\) from the positive \(\boldsymbol{x}\) -axis to the vector \(O P\) that corresponds to a. $$\mathbf{a}=-3 \mathbf{i}+7 \mathbf{j}$$

A constant force of magnitude 10 has the same direction as - i. Find the work done if its point of application moves from \(P(0,1)\) to \(Q(1,0)\)

Exer. 35-40: Prove the property if a and b are vectors and \(m\) is a real number. $$\mathbf{a} \cdot \mathbf{a}=\|\mathbf{a}\|^{2}$$

Find the magnitude of the vector a and the smallest positive angle \(\boldsymbol{\theta}\) from the positive \(\boldsymbol{x}\) -axis to the vector \(O P\) that corresponds to a. $$\mathbf{a}=6 \mathbf{i}-5 \mathbf{j}$$

Express the complex number in trigonometric form with \(0 \leq \theta<2 \pi\) $$6 i$$