Manuals/calci/COMPLEX

COMPLEX(rn,in,sf)

• $rn$ is the real number.
• $in$ is the imaginary number.
• $sf$ is the suffix for the imaginary number.

Description

• COMPLEX function converts the real and imaginary coefficients into a complex number.
• A complex number is a combination of a real and an imaginary number.
• A number which is positive or negative, rational or irrational or decimals are called real numbers.
• An Imaginary number is a number that when squring it gives a negative result.
• For e.g. ${-4}^{2}=16$. Because a negative times a negative is positive.
• A complex number is a number is in the form $z=a+bi$, where $a$ and $b$ are real numbers and $i$ is the imaginary unit. Where $i={\sqrt {-1}}$
• In $COMPLEX(rn,in,sf)$, here $rn$ is the real part of a complex number, $in$ is the imaginary part of a complex number and $sf$ is the imaginary unit of a complex number like $i$ or $j$.
• To mention $i$ and $j$, we must use the lower case only
• In a complex number $z$ real part is denoted by $Re(z)$ & imaginary part is denoted by $Im(z)$.
• COMPLEX returns the error value, when $rn$ and $in$ are non-numeric.
• Suffix $sf$ should be either $i$ or $j$, otherwise it shows error value.
• A Complex number whose real part is zero is said to be purely imaginary.
• A Complex number whose imaginary part is zero is a real number. In that cases we have to assign '0' for that part.
  • $=COMPLEX(5,2)$ gives $5+2i$
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle =COMPLEX(5,2,"j")} gives $5+2j$

ZOS Section

• The syntax is to calculate COMPLEX in ZOS is $COMPLEX(REAL,IMAGINARY,SUFFIX)$
• $REAL$ is the real part.
• $IMAGINARY$ is the imaginary part.
• $SUFFIX$ is imaginary unit which is either "i" or "j".
• E.x: COMPLEX(-1..1,10..11,"j")

Examples

Complex(rn,in,sf)	rn	in	sf	RESULT
Complex(5,6)	5	6		5+6i
Complex(5,2,"j")	5	2	j	5+2j
Complex(2,0,"i")	2	0	i	2
Complex(0,-4,i)	0	-4	i	-4i
Complex(5,"j")	5		j	Error

See Also

• IMAGINARY
• IMREAL

References

Complex Numbers