Question

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

Answer 1

Hint: To solve this type of problem we have to multiply the two terms and apply formulas to solve for the standard form. Multiplication of two terms and solving is the main step.

Complete step-by-step answer:
Given $(1+i)(1+2i)$
We have to solve by multiplication of both the terms, $(1+i)(1+2i)$
The expression appears as follows,
$(1+i)(1+2i)$
By solving further we get,
$1+i+2i+2{{i}^{2}}$. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (a)
We know that ${{i}^{2}}$= -1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (b)
Now by substituting (b) in (a) we get,
$1+i+2i+2(-1)$
Further solving the above expression we get,
$1+i+2i-2$
Further solving the above expression we get,
$1-2+i+2i$
$=-1+3i$ which is in the form of $a+ib$.

Note: This is a direct problem which just requires the multiplication of the two expressions. The value of a and b can be any number either rational, whole etc. Therefore while writing the definition of complex numbers we write $a,b\in R$.