Question

Express the complex number (1 + i)(1 + 2i) in the standard form of (a + ib).

Answer 1

Hint: We have to open the brackets of the given equation in the question and then we compare the following to the general term of a complex number which is a + ib. We use the following formula to expand the bracket (a + ib)(c + id) = ac – bd + i(bc + ad )

Complete step-by-step answer:

Complex numbers are numbers which are represented on the imaginary plane. They are represented in the following number: a + ib, where a denotes the real part of the complex number and b denotes the imaginary part.

Some of the basic identities we need to remember before we proceed into the question are
${{i}^{2}}$ = -1
${{i}^{3}}$ = -i
${{i}^{4}}$ = 1

With these in mind, let us proceed with the question:

When we open the brackets of the 2 complex numbers, we treat them like any 2 variables and cross multiply while keeping above identities in mind.

We use the following formula to expand the bracket (a + ib) (c + id) = ac – bd + i (bc + ad)

Applying the formula, we get:

(1 + 2i) (1 + i) = [1-2 +i(2+1)].

= - 1 + 3i.

So, (1 + i) (1 + 2i) in the standard form is -1 + 3i.

Note: While doing simplification of complex numbers keep in mind that all rules are the same when it is considered with real numbers only difference is that the real terms are dealt separately and the imaginary part is dealt separately. Only thing that connects them are the basic identities written above.