Question

what is the standard form of ( 1 + i )( 1 + 2i )

Answer 1

hope this help u bro

Answer 2

The Standard Form of a Complex Number is:

$z = a+i \, b$

Where $a$ and $b$ both are Real Numbers, and $i = \sqrt{-1}$

Here, we can bring the question in standard form as follows:

$(1+i)(1+2i) \\ \\ = (1\times 1) + (1\times 2i) + (i \times 1) + (i\times 2i) \\ \\ = 1 + 2i + i + 2i^2 \\ \\ \left[ \, Now \, \, i^2=-1 \, \right] \\ \\ \\ = 1 + 3i + 2(-1) \\ \\ = 1+3i-2 \\ \\ = -1+3i$


Thus, The Standard Form of (1+i)(1+2i) is $\bold{-1+3i}$.