Question

Real part of the complex number (1+2i)(-2+i) is ______ *
2 points
-4
-3
-7
4​

Answer 1

Answer:

-4

Step-by-step explanation:

(1+2i)(-2+i)=-2+i-4i+2i^2=-2-3i-2=-4-3i

so real part is -4

Answer 2

The real part of the complex number (1 + 2i)(-2 + i) is -4. (Option A)

Given,

f(x) = (1+2i)(-2+i)

To find,

The real part of the complex number f(x)

Solution,

We can simply solve the mathematical problem by the following procedure.

We know by the concepts of complex numbers that i² = -1.

Now,

f(x) = (1 + 2i)(-2 + i)

On opening the brackets and simplifying the complex number;

f(x) = -2 + i - 4i + 2i²

      = -2 - 3i - 2

      = - 4 - 3i

Now,

We know that any complex number is in the form of x + iy, where x is the real part of the complex number and y is the imaginary part of the complex number.

On comparing the simplified f(x) with the general form of the complex numbers.

x + iy = -4 - 3i

Thus,

x = -4

y = -3

As a result, we can state that the real part of the complex number f(x)  (1 + 2i)(-2 + i) is -4. (Option A)