IMARGUMENT Function in Zoho Sheet: Syntax and Worked Examples

• Introduced: Listed in Zoho Sheet’s current function reference; the first introduction date or release remains unknown.
• Availability: Currently documented in the rolling web-service help; no final supported-version endpoint is established.
• Scope: Web documentation is the checked source. Mobile parity, old workbook behavior and exact imported-text handling are not separately established.
• Checked: October 14, 2026, against the official IMARGUMENT entry. Examples independently calculated; no native Zoho Sheet test.

=IMARGUMENT(complex_number)

The single required argument is text representing a complex number. Zoho defines the argument as the angle in the representation a+bi = r*(cos(angle)+i*sin(angle)). The result is in radians; the function has no optional degrees mode.

For 3+4i, the real coefficient is 3, the imaginary coefficient is 4, and the magnitude is 5. None of those three numbers is the angle. The angle describes direction relative to the positive real axis.

A literal is quoted inside a formula, as in =IMARGUMENT("3+4i"). In a referenced cell, type the text 3+4i without enclosing quotes and use =IMARGUMENT(A2). COMPLEX can construct such inputs from two numeric coefficients instead of manual concatenation.

In a blank worksheet, put Complex value, Radians, and Degrees in A1:C1. Type the following text in A2:A7 without enclosing quotes:

In B2, enter =IMARGUMENT(A2) and fill through B7. In C2, enter =DEGREES(B2) and fill through C7. DEGREES converts radians to degrees; merely formatting B as a number does not change its angular unit.

The first three cases agree with Zoho’s published examples. The other cases use the same mathematical angle convention in the right half-plane. The negative angles in rows 3 and 6 correspond to negative imaginary coefficients there, while 5j points along the positive imaginary axis.

For a positive real coefficient, the angle is consistent with the arctangent of imaginary divided by real. That shortcut is not a general replacement for a complex argument function: a pure imaginary value has real coefficient zero, and inputs in different quadrants can share the same quotient.

Use IMARGUMENT on the original complex value rather than discarding sign information or dividing by zero. The short reference does not enumerate the returned interval’s endpoints, signed-zero behavior or all negative-real-axis cases. Those branch-boundary details should be checked in the intended client rather than inferred from this six-row table.

Continue in the same worksheet. Label D1:F1 Magnitude, Rebuilt real, and Rebuilt imaginary. Enter:

• D2: =IMABS(A2)
• E2: =D2*COS(B2)
• F2: =D2*SIN(B2)

Fill D2:F2 through row 7. IMABS supplies the magnitude, while COS and SIN use the radian angle directly. Expected reconstructed coefficient pairs are (2,3), (1,-4), (0,5), (3,4), (4,-3), (1,1), allowing tiny numerical residuals such as a value near zero instead of exact zero.

In G2 enter =E2-IMREAL(A2) and in H2 =F2-IMAGINARY(A2). Fill through G7:H7. These residuals should be close to zero for the listed cases. Comparing coefficients from IMREAL and IMAGINARY is more informative than comparing formatted text strings.

Use B’s radians in the reconstruction, not C’s degrees. Passing 53.1301 directly to COS would mean 53.1301 radians, not 53.1301 degrees. Also retain the unrounded B result rather than retyping the table’s printed decimal.

On a separate blank worksheet, put 3+4i in A2 and 6+8i in A3. Use =IMARGUMENT(A2) in B2 and fill to B3: both angles are approximately 0.9272952180. Use =IMABS(A2) in C2 and fill to C3: the magnitudes are 5 and 10.

Multiplying both coefficients by a positive factor preserves direction while changing length. This is useful when a report needs separate columns for amplitude and phase instead of one ambiguous complex-text column.

The zero complex number has no unique mathematical direction. Zoho’s short page does not specify a complete zero-input result or its error token, so exclude it from this angle workflow unless the intended environment has been checked.

Malformed text, uppercase suffixes, missing quotes, broken references and mixed locale punctuation should be diagnosed separately. The generic error list is not a guarantee of one specific outcome for every malformed input. Use valid lowercase i/j text and do not turn every error into zero, which would falsely imply a direction along the positive real axis.