Algebra of Complex Numbers

$z_1=3+i \& z_2=4+i$. Find $z_1{z}_2$ multiplied with multiplicative identity of all complex numbers.

$z_1=3-i \& z_2=4-i$. Find $z_1{z}_2$ multiplied with multiplicative identity of all complex numbers.

$z_1=3-2i \& z_2=2-3i$. Find $z_1{z}_2$ multiplied with multiplicative identity of all complex numbers.

$z_1=3+2i \& z_2=2+3i$. Find $z_1{z}_2$ multiplied with multiplicative identity of all complex numbers.

$z_1=1+2i \& z_2=2+5i$. Find $z_1{z}_2$ multiplied with multiplicative identity of all complex numbers.

$z_1=4i-2 \& z_2=3-2i$. Add $z_1+z_2$ to additive identity of both complex numbers.

$z_1=5i-1 \& z_2=4-3i$. Add $z_1+z_2$ to additive identity of both complex numbers.

$z_1=5i+1 \& z_2=4+3i$. Add $z_1+z_2$ to additive identity of both complex numbers.

$z_1=3+2i \& z_2=2+3i$. Add $z_1+z_2$ to additive identity of both complex numbers.

$z_1=1+2i \& z_2=2+5i$. Add $z_1+z_2$ to additive identity of both complex numbers.

$z_1=2-3i \& z_2=1-2i$. Verify commutative property of addition of complex numbers.

$z_1=2-3i \& z_2=1+4i$. Verify commutative property of addition of complex numbers.

$z_1=3+5i \& z_2=2+4i$. Verify commutative property of addition of complex numbers.

$z_1=1+4i \& z_2=2+3i$. Verify commutative property of addition of complex numbers.

$z_1=1+2i \& z_2=2+5i$. Verify commutative property of addition of complex numbers.

$z_1=2+i$ and $z_2=2-i$. Prove the closure property of multiplication of two complex numbers.

$z_1=2+i$ and $z_2=1+i$. Prove the closure property of multiplication of two complex numbers.

$z_1=2+5i$ and $z_2=3+4i$. Prove the closure property of multiplication of two complex numbers.

$z_1=1+3i$ and $z_2=2+3i$. Prove the closure property of multiplication of two complex numbers.

$z_1=1+2i$ and $z_2=2+5i$. Prove the closure property of multiplication of two complex numbers.