Examples for

Complex Numbers

Complex numbers are numbers of the form a + ⅈb, where a and b are real and ⅈ is the imaginary unit. They arise in many areas of mathematics, including algebra, calculus, analysis and the study of special functions, and across a wide range of scientific and engineering disciplines. Oftentimes, they form connections between fields, for example with Euler's formula, which relates imaginary numbers to trigonometry and exponentiation. Use Wolfram|Alpha’s power and computational understanding to work with complex numbers, as well as the larger area of complex analysis, and to express them in different forms.
Complex Numbers

Do computations with complex numbers, from basic arithmetic to finding roots and solving equations.

Do basic arithmetic on complex numbers:

(2+3i)(5-i)
1/(12+7i)
((3+4i)/5)^10

Find roots of complex numbers:

sqrt(i)
(1+i)^(1/5)

Find all complex n th roots of a number:

all 12th roots of 2

Apply functions to complex numbers:

exp(24+2i)

Do computations that give complex numbers as a result:

log (-1)
arcsin 2

Convert complex numbers to and from different representational forms:

1+I from Cartesian to polar form
exp(pi/4 i) to polar trigonometric form
cos(pi/3)+sin(pi/3)I from polar trigonometric to polar exponential form
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