Question

urgent please help!
write the standard form of a complex number giving two examples

Answer 1

any complex number?

Answer 2

yes

Answer 3

i vote for \(2+3i\) but you can make up your own

Answer 4

is that the complex or standard version?

Answer 5

i sense some confusion here

Answer 6

there is no such thing as "complex" or "standard" version
there is "standard form" for a complex number, which is \(a+bi\)

Answer 7

so for example \(2+3i\) is in standard form, but
\[\frac{2+3i}{5}\] is not

Answer 8

\(\frac{1+\sqrt{3}i}{2}\) is not standard form, but \(\frac{1}{2}+\frac{\sqrt{3}}{2}i\) is

Answer 9

A complex number is a number that has both a real part and an imaginary part.
If \(z\) is a complex number ; it can be written in this form
\[z=a+ib\]
where \(a\) and \(b\) are both real numbers

\(a={\frak{R}}( z) \) is the real part of \(z\)
and \(b={\frak{I}}( z) \) is the imaginary part of \(z\)


When the number has no imaginary component \(b=0\) and we call this number a real number \(z\in \mathbb R\).

When the number has no real component \(a=0\) and we call this number a purely imaginary number \(z\in \mathbb I\).

When neither \(a\) nor \(b\) are zero the number has both a real part and an imaginary part. Only these numbers are complex \(z\in \mathbb C\)

So to construct a complex number just choose two non zero real numbers,
multiply one by the imaginary constant \(i\), and add them.