Casio fx-570MS Complex Numbers: Modes and Checks

Enter complex-number mode deliberately

The fx-570MS uses CMPLX mode for supported complex-number calculations. Casio's manual distinguishes rectangular a+bi input from polar r∠θ input and explains how results are displayed. A result may require switching between its real and imaginary parts rather than expecting both components to appear together. Consult the key labels for the exact edition in your hands. Ordinary real-number mode is not a substitute for CMPLX mode when an expression requires the imaginary unit i, defined by i²=−1. Check the mode before diagnosing an apparent arithmetic failure.

Verify addition component by component

For z₁=4+3i and z₂=1−2i, addition gives z₁+z₂=(4+1)+(3−2)i=5+i. Subtraction gives z₁−z₂=(4−1)+(3+2)i=3+5i. The negative imaginary part of the second number must stay inside the subtraction. This is a useful first test because each component can be checked mentally. A displayed real part of 5 alone does not establish the entire sum; inspect the imaginary part as well. Write the complete result in a+bi form when transferring it to working or a report.

Multiply using i squared equals minus one

For the same pair, (4+3i)(1−2i)=4−8i+3i−6i²=10−5i. The real part includes the contribution from −6i², which becomes +6. Multiplying only the real components and only the imaginary components would miss the cross terms. Enter both full complex numbers with parentheses when needed to preserve the expression. The linked Complex Number Calculator can independently check the operation using real and imaginary component fields. Use 4 and 3 for the first number, 1 and −2 for the second, and choose multiplication.

Divide by multiplying by the conjugate

To calculate (4+3i)/(1−2i), multiply numerator and denominator by 1+2i. The denominator becomes 1²+2²=5, and the numerator becomes −2+11i. The quotient is therefore −0.4+2.2i. Check by multiplying the quotient by the original divisor: (−0.4+2.2i)(1−2i)=4+3i. That reconstruction tests both signs and both components. Division by 0+0i is undefined. A nonzero imaginary component still makes a divisor nonzero even when its real part is zero, so inspect the complete number.

Interpret magnitude and angle correctly

The magnitude of 3+4i is √(3²+4²)=5. Its argument is approximately 53.1301 degrees, or 0.927295 radians, placing it in the first quadrant. These values describe the same number in polar form. The angle unit matters for polar input and output, while a rectangular entry such as 3+4i already specifies its components directly. For a number in another quadrant, a plain arctangent of imaginary part divided by real part can select the wrong angle unless quadrant information is handled. Check the signs of both components against the reported direction.

Do not confuse conjugation with negation

The conjugate of 4+3i is 4−3i, whereas its negative is −4−3i. Multiplying a number by its conjugate produces its squared magnitude: (4+3i)(4−3i)=25. Multiplying by its negative instead produces a different complex quantity. These distinctions matter in impedance calculations, roots and complex division. If a stored result is reused, confirm whether the next command expects the original number, its conjugate, its reciprocal or its magnitude. The names describe separate operations, even when a particular example happens to produce similar-looking digits.

Check scope when comparing tools

This site's Complex Number Calculator supports the displayed two-number arithmetic operations with separate real and imaginary inputs. It does not simulate all fx-570MS functions, variable restrictions or polar-format controls. Compare the addition, multiplication or division examples above using those fields, and use the official Casio manual for model-specific operations and display switching. Retain full intermediate values when practical and round the final components consistently. A reliable comparison records the expression, angle unit where relevant, operation and both components of the result, rather than matching only one number shown on a screen.

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