Question

(-√3+√-2) (2√3-i) complex number express in a+ib


​

Answer 1

Step-by-step explanation:

complex number problems i²= -1

Answer 2

The answer is (√2-6)+i√3(1+2√2)

Step-by-step explanation:

COMPLEX NUMBER : Complex number contains real numbers and imaginary numbers(i)

we know that i² = -1

GIVEN EXPRESSSION:

Equation 1 = (-√3+√-2)

Equation 2=  (2√3-i)

Multiply the two given equation

STEP 1:

Multiply -√3 to the second equation

we obtain,

==> -√3  (2√3-i)

==> ( -√3)(2√3)-(-√3i)

==> -2(√3√3)+√3i

==> -2(3)+√3i

==> -6+√3i

STEP 2:

Expand √-2

We can written √-2 as  $\sqrt{-1 X2}$

we know that i² = -1

Substitute i² instead of -1

==> $\sqrt{i^{2} X2}$

==> $i\sqrt{2} or \sqrt{2}i$

STEP 3:

Multiply √2i to the second equation

==> ( √2i)(2√3-i)

==> ( (√2i)(2√3)-(√2i)(i))

==> 2√6i-√2i²

we know that i²=-1

==> 2√6i-√2(-1)

==> 2√6i+√2

STEP 4:

Add STEP 1 and STEP 3

==> -6+√3i+ 2√6i+√2

Separate real and imaginary parts

==> √3i+ 2√6i+√2-6

==> Taking √3 as common for imaginary part

==> (√2-6)+√3i(1+2√2)

==> (√2-6)+i√3(1+2√2)

Real Part = √2-6

Imaginary part = √3(1+2√2)