Complex Numbers Complex numbers can be entered in any of 3 different formats:Cartesian.Polar.Via Euler's Identity. Output can also be in any of these 3 formats by making a selection in the 'Settings' – the default output setting is Cartesian - once the "=" button has been pressed, the Mode button can be used to show the result in each of the other formats. Entries are made as follows: CartesianComplex numbers consisting of real and imaginary parts must be entered in parentheses in the format a + bi or a - bi where "a" is the real part and "b" is the imaginary part – hence a complex number 2 + 3i would be entered as (2 + 3i) – if, for example 3i is entered without surrounding parentheses, the real part will be assumed to be zero – similarly, if (2 × 3i) is entered, the calculation required will be assumed to be a real number 2 multiplied by a complex number 3i which has a real part of zero. PolarUse the cis button to enter complex numbers in polar form where the cisθ function is a shorthand way of writing the equivalent expression cosθ + i.sinθ – entries are made in the format r cis θ where r is the modulus and θ is the phase angle in radians (can be changed to degrees in the Settings if required - the output will then also be in degrees). Via Euler's IdentityUse the ei button to enter complex numbers via Euler's Identity where eiθ is a shorthand way of writing the equivalent expression cosθ + i.sinθ – entries are made in the format r eiθ where r is the modulus and θ is the phase angle in radians (can be changed to degrees in the Settings if required - the output will then also be in degrees). In addition to trigonometric, log, power and square root functions, the complex number screen also includes the abs function, which returns the absolute value of a complex number, and the exp function, which implements the exponential function ex for the complex number.
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