Complex multiplication is closed : Product or quotient of two complex number is another complex number

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What does 'closure' mean?

- closed
- not open
- both the above
- both the above

Answer is 'both the above'

Given complex numbers `z_1=a_1+b_1i` and `z_2=a_2+b_2i`, `a_1,a_2,b_1,b_2 in R`, will `z_1 xx z_2` a complex number?

- No. When multiplied, the result has `i^2`
- Yes. When multiplied, the result consists of real numbers, as real and imaginary parts
- Yes. When multiplied, the result consists of real numbers, as real and imaginary parts

The answer is 'Yes. When multiplied, the result consists of real numbers as real and imaginary parts'

• Product or quotient of two complex number is another complex number - closed

**Closure property of Multiplication and Division: ** For any given complex numbers `z_1, z_2 in CC`, ` z_1 xx / -: z_2 in CC`.

*Solved Exercise Problem: *

Given complex numbers `z_1=a_1+b_1i` and `z_2=a_2+b_2i`, `a_1,a_2,b_1,b_2 in R`, will `z_1 -: z_2` a complex number?

- No. Complex division is not defined
- Yes. complex number division is equivalently multiplication by the conjugate
- Yes. complex number division is equivalently multiplication by the conjugate

The answer is 'Yes. When multiplied, the result consists of real numbers as real and imaginary parts'

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