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manual:chapter3:complex [2017/06/17 14:02]
smartin [Complex number arithmetic] |
manual:chapter3:complex [2017/07/05 19:30]
smartin [Entering complex numbers] |
| ==== Entering complex numbers ==== | ==== Entering complex numbers ==== |
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| A complex number can be represented mathematically in rectangular form as $z = x + iy$ or in polar form as $z = re^{i\theta}$. A complex number is entered as a pair of numbers comma or space separated and enclosed in parenthesis. For example, the complex number $5+3i$ would be entered (in rectangular form) as ''(5, 3)'' or ''(5 3)'' or in polar form ($r,\theta$) as ''(5.83, ∡30.96)''((The keyboard shortcut for the angle symbol (∡) is **AL-RS-6**.)). Alternatively, a complex number can be created from two numbers on the stack using the command ''R→C'': | A complex number can be represented mathematically in rectangular form as $z = x + iy$ or in polar form as $z = re^{i\theta}$. A complex number is entered as a pair of numbers comma or space separated and enclosed in parenthesis. For example, the complex number $5+3i$ would be entered (in rectangular form) as ''(5, 3)'' or ''(5 3)'' or in polar form ($r,\theta$) as ''(5.83, ∡30.96)''((The keyboard shortcut for the angle symbol (∡) is **AL-RS-6**. In this case the calculator is set to ''DEG'' mode, angles can be expressed in radians by setting ''RAD''.)). Alternatively, a complex number can be created from two numbers using the command ''R→C'': |
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| ''5 3 R→C'' | ''5 3 R→C'' |
| leads to ''(#101b,#11b)'' on the stack, but taking the complex conjugate (''CONJ'') results in ''(5,-3)''. | leads to ''(#101b,#11b)'' on the stack, but taking the complex conjugate (''CONJ'') results in ''(5,-3)''. |
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| System flag -103 formally sets the calculator mode to complex: ''-103 SF''. | System flag -103 formally sets the calculator mode to complex: ''-103 SF''. This is important to ensure all input to functions return complex results. For example, without setting flag -103, taking the square root of -1 results an an error (Argument outside domain). Whereas in complex mode, the square root of -1 returns the correct result ''(0,1)''. |
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| The following table summarizes commands applicable to complex numbers, $z=x+iy=re^{i\theta}$. | The following table summarizes commands applicable to complex numbers, $z=x+iy=re^{i\theta}$. |
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| | Command | Purpose | Example | | | Command | Purpose | Example ($\theta$ in degrees) | |
| | ''C→R'' | Break down complex number to two reals | ''(5,3) C→R'' yields ''(5,3)'' ''5'' ''3''| | | ''C→R'' | Break down complex number to two reals | ''(5,3) C→R'' yields ''(5,3)'' ''5'' ''3''| |
| | ''R→C'' | Combine two numbers to a complex | ''5 3 R→C'' yields ''(5,3)''| | | ''R→C'' | Combine two numbers to a complex | ''5 3 R→C'' yields ''(5,3)''| |
| | ''→RECT'' | Convert from polar to rectangular | ''(5.831.,∡30.964.°) →RECT'' yields ''(5.,3.)''| | | ''→RECT'' | Convert from polar to rectangular | ''(5.831.,∡30.964.°) →RECT'' yields ''(5.,3.)''| |
| | ''ABS'' | $|z|=r=\sqrt{x^2+y^2}$ | ''(5,3) ABS'' yields ''5.831.''| | | ''ABS'' | $|z|=r=\sqrt{x^2+y^2}$ | ''(5,3) ABS'' yields ''5.831.''| |
| | ''ARG'' | $\theta = atan(y/x)$ | ''(5,3) ARG'' yields ''∡30.964.°''| | | ''ARG'' | $\theta = \operatorname{atan}(y/x)$ | ''(5,3) ARG'' yields ''∡30.964.°''| |
| | ''SIGN'' | $z/|z|$ | ''(5,3) SIGN'' yields ''(0.857.,0.514.)''| | | ''SIGN'' | $z/|z|$ | ''(5,3) SIGN'' yields ''(0.857.,0.514.)''| |
| | ''NEG'' | $-z=-x-iy$ | ''(5,3) NEG'' yields ''(-5, -3)''| | | ''NEG'' | $-z=-x-iy$ | ''(5,3) NEG'' yields ''(-5, -3)''| |