Section 1
Introduction
Express each of the complex number given in the form $a+i b$.$$(5 i)\left(-\frac{3}{5} i\right)$$
Express each of the complex number given in the form $a+i b$.$$i^{9}+i^{19}$$
Express each of the complex number given in the form $a+i b$.$$i^{-39}$$
Express each of the complex number given in the form $a+i b$.$$3(7+i 7)+i(7+i 7)$$
Express each of the complex number given in the form $a+i b$.$$(1-i)-(-1+i 6)$$
Express each of the complex number given in the form $a+i b$.$$\left(\frac{1}{5}+i \frac{2}{5}\right)-\left(4+i \frac{5}{2}\right)$$
Express each of the complex number given in the form $a+i b$.$$\left[\left(\frac{1}{3}+i \frac{7}{3}\right)+\left(4+i \frac{1}{3}\right)\right]-\left(-\frac{4}{3}+i\right)$$
Express each of the complex number given in the form $a+i b$.$$(1-i)^{4}$$
Express each of the complex number given in the form $a+i b$.$$\left(\frac{1}{3}+3 i\right)^{3}$$
Express each of the complex number given in the form $a+i b$.$$\left(-2-\frac{1}{3} i\right)^{3}$$
Find the multiplicative inverse of each of the complex numbers given.$$4-3 i$$
Find the multiplicative inverse of each of the complex numbers given.$$\sqrt{5}+3 i$$
Find the multiplicative inverse of each of the complex numbers given.$$-i$$
Express the following expression in the form of $a+i b$ :$$\frac{(3+i \sqrt{5})(3-i \sqrt{5})}{(\sqrt{3}+\sqrt{2} i)-(\sqrt{3}-i \sqrt{2})}$$