Find the product of the complex numbers.Leave answers in polar form. z_1 = 1 + i z_2 = -1 + i

Find the product of the complex numbers.Leave answers in polar form. z_1 = 1 + i z_2 = -1 + i

Question
Complex numbers
asked 2021-02-26
Find the product of the complex numbers.Leave answers in polar form.
\(\displaystyle{z}_{{1}}={1}+{i}\)
\(\displaystyle{z}_{{2}}=-{1}+{i}\)

Answers (1)

2021-02-27
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 \(\displaystyle-{2}{\left({{\cos{{0}}}^{\circ}+}{i}{\sin{{0}}}^{\circ}\right)}\)
0

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