To find the product of the given complex numbers.

Solution:

The product for the complex numbers can be calculated as

\(\displaystyle{z}_{{1}}\cdot{z}_{{2}}={\left({1}+{i}\right)}\cdot{\left(-{1}+{i}\right)}={i}^{{2}}-{1}^{{2}}=-{1}-{1}=-{2}\)

The product of the complex numbers is obtained as, (−2) and can be written in polar form as,

\(\displaystyle{z}_{{1}}\cdot{z}_{{2}}=-{2}{z}_{{1}}\cdot{z}_{{2}}=-{2}{\left({{\cos{{0}}}^{\circ}+}{i}{\sin{{0}}}^{\circ}\right)}\)

Hence, the product for the given complex numbers is obtained as \(\displaystyle-{2}{\left({{\cos{{0}}}^{\circ}+}{i}{\sin{{0}}}^{\circ}\right)}\)

Solution:

The product for the complex numbers can be calculated as

\(\displaystyle{z}_{{1}}\cdot{z}_{{2}}={\left({1}+{i}\right)}\cdot{\left(-{1}+{i}\right)}={i}^{{2}}-{1}^{{2}}=-{1}-{1}=-{2}\)

The product of the complex numbers is obtained as, (−2) and can be written in polar form as,

\(\displaystyle{z}_{{1}}\cdot{z}_{{2}}=-{2}{z}_{{1}}\cdot{z}_{{2}}=-{2}{\left({{\cos{{0}}}^{\circ}+}{i}{\sin{{0}}}^{\circ}\right)}\)

Hence, the product for the given complex numbers is obtained as \(\displaystyle-{2}{\left({{\cos{{0}}}^{\circ}+}{i}{\sin{{0}}}^{\circ}\right)}\)