Manuals/calci/IMPRODUCT

IMPRODUCT(z1,z2,z3)

• $z1,z2,z3$ are the complex numbers of the form $a+ib$

Description

• This function gives the product of the complex numbers.
• In IMPRODUCT(z1,z2,z3,…), where z1,z2,z3,... are the complex numbers and is in the form of $a+ib$.
• where $a$ & $b$ are the real numbers. $i$ is the imaginary unit .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}} .
• The multiplication of two complex numbers is a complex number.
• Let 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 z1=a+ib} and 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 z2=c+id} .
• Then the product of two complex number is 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 z1.z2=(a+ib)(c+id)=(ac-bd)+(ad+bc)i} .
• In this function 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 z1} is required. 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 z2,z3,...} are optional.
• We can use COMPLEX function to convert real and imaginary number in to a complex number.

Examples

1. =IMPRODUCT("1+3i","5+2i") = -1+17i
2. =IMPRODUCT("i","3-i") = 1+3i
3. =IMPRODUCT("5","-2+4i") = -10+20i
4. =IMPRODUCT("2+3i","4+6i","3+5i") = -150+22i
5. =IMPRODUCT("-6-2i","-1-i") = 4+8i

See Also

• IMREAL
• IMSUM
• IMAGINARY
• COMPLEX

References

• Imaginary number
• Dot product