ringearV

2021-02-26

Find the product of the complex numbers.Leave answers in polar form.

${z}_{1}=1+i$

${z}_{2}=-1+i$

Laaibah Pitt

Skilled2021-02-27Added 98 answers

To find the product of the given complex numbers.

Solution:

The product for the complex numbers can be calculated as

${z}_{1}\cdot {z}_{2}=(1+i)\cdot (-1+i)={i}^{2}-{1}^{2}=-1-1=-2$

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

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

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

Solution:

The product for the complex numbers can be calculated as

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

Hence, the product for the given complex numbers is obtained as