Manuals/calci/IMAGINARY

IMAGINARY(z)

• 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 z} is the complex number is in the form 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 a+bi} .

Description

• This function gives the imaginary coefficient of a complex number.
• Imaginary number is a real number which is multiplied with the imaginary unit $i$, where 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 i=\sqrt{-1}} .
• When imaginary number 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 bi} is get adding to the real number 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 a} , then it forms a complex number.
• Also when we are squaring the imaginary number 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 bi} , it will give the negative real number 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 {-b}^2} .
• For eg 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 (5i)^2=-25} . We can use COMPLEX function to convert the real and imaginary coefficients to a complex number.
• A complex number is a imaginary number when the real part is zero.

Examples

IMAGINARY("2+3i")=3 
IMAGINARY("4-5i")=-5
IMAGINARY("3j")=3
IMAGINARY("7")=0

Equation	Real Part	Imaginary Part	Result(Imaginary)
=IMAGINARY("2+3i")	2	3i	3
=IMAGINARY("4-5i")	4	-5i	-5
=IMAGINARY("3j")	0	3j	3
=IMAGINARY("7")	7	0	0

See Also

• COMPLEX
• IMREAL

References

Imaginary Number