Question

If `u=(1+isqrt(3))` and `v=(1+2isqrt(3))`, what is uv?

Answer 1

$u=(1+i\sqrt3),\ v=(1+2i\sqrt3)\\\\uv=(1+i\sqrt3)(1+2i\sqrt3)\\\\=(1)(1)+(1)(2i\sqrt3)+(i\sqrt3)(1)+(i\sqrt3)(2i\sqrt3)\\\\=1+2i\sqrt3+i\sqrt3+2i^2(\sqrt3)^2\\\\=1+3i\sqrt3+2(-1)(3)\\\\=1+3i\sqrt3-6\\\\=\boxed{-5+3i\sqrt3}$

Answer 2

The product of the two complex number u = ( 1 + i√3) and v = ( 1 + 2i√3) will be -5 + 3i√3.

What is a complex number?

A complex number is the combination of real and imaginary numbers.

The formation of a complex number looks like a + ib where part a is called real and part ib is called imaginary.

In another word, complex numbers are the number in which a term I called iota present and the value of this term is under the root of -1.

Given that

u = ( 1 + i√3)  and v = ( 1 + 2i√3)  now

u × v = ( 1 + i√3) × ( 1 + 2i√3)

u × v = 1( 1 + 2i√3) +  i√3( 1 + 2i√3)

u × v = 1 + 2i√3 +  i√3 + 2i²×3

u × v = -5 + 3i√3 ( since i² = -1)

For more about complex number

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