IMLOG2 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 IMLOG2 entry. Examples independently calculated; no native Zoho Sheet test.

=IMLOG2(complex_number)

The sole argument is required complex-number text or a reference containing that text. There is no optional base argument: IMLOG2 already selects base 2. Use IMLOG10 for the other listed base, or IMLN for the natural complex logarithm.

For the nonzero values used here, the independent logarithm model is:

Real coefficient = LN(magnitude) / LN(2)
Imaginary coefficient = angle in radians / LN(2)

Thus the imaginary coefficient is a scaled angle, not the angle itself. The mathematical branch used for these examples agrees with Zoho’s published right-half-plane and positive-imaginary-axis examples. The short entry does not specify every branch endpoint or signed-zero convention.

Use lowercase i or j in valid complex text. Inside a formula, quote a literal such as “2+3j”; in a worksheet cell, enter 2+3j without enclosing quote characters. COMPLEX can build the text from numeric coefficients and a chosen suffix.

In a blank worksheet, set A1:D1 to Complex input, Complex log, Real coefficient, and Imaginary coefficient. Enter the text below in A2:A7:

Put =IMLOG2(A2) in B2 and fill through B7. Then enter =IMREAL(B2) in C2 and =IMAGINARY(B2) in D2, filling both through row 7. Format C:D as ordinary numbers with eight decimal places; B remains the complex result.

The first three inputs and coefficients agree with Zoho’s direct examples. Separate numeric helpers avoid treating insignificant string formatting differences as calculation errors. The displayed precision is not a promise that the application emits exactly that many characters.

Rows 4, 5 and 6 all have magnitude 5 but different directions. Their real log coefficients agree, while their imaginary coefficients differ. Taking only the real part would intentionally discard that direction information.

Leave A:D intact. In E1:F1 use Real from IMLN and Imaginary from IMLN. In E2 enter =IMREAL(IMLN(A2))/LN(2); in F2 enter =IMAGINARY(IMLN(A2))/LN(2). Fill through row 7.

E should agree with C, and F with D, to the displayed precision for these cases. Here LN receives the positive real number 2; IMLN receives the complex input. This keeps real and complex logarithms in their appropriate roles.

For a phase check, put =D5*LN(2) in H5. It recovers approximately 0.9272952180 radians for the input 3+4i in A5. IMARGUMENT gives that angle directly. Keep D5’s full stored coefficient for this reconstruction.

On a separate blank worksheet named Scaling, put Original, Doubled, Original log2, Doubled log2, Real change, and Imaginary change in A1:F1. Type 3+4i in A2. Enter:

• B2: =IMPRODUCT(A2;COMPLEX(2;0;"i")), representing 6+8i.
• C2: =IMLOG2(A2)
• D2: =IMLOG2(B2)
• E2: =IMREAL(D2)-IMREAL(C2), expected approximately 1.
• F2: =IMAGINARY(D2)-IMAGINARY(C2), expected approximately 0.

IMPRODUCT multiplies the complex value by a positive real factor constructed with COMPLEX. The magnitude rises from 5 to 10. Base-2 logarithms convert that doubling into an increase of one in the real coefficient: approximately 2.3219280949 becomes 3.3219280949.

Both values retain the same direction, so their imaginary coefficients remain approximately 1.3378042125. The identity is limited here to positive real scaling; multiplying by an arbitrary complex number can change the angle and may cross a branch boundary.

• Only a real logarithm was expected: inspect whether the original value has a nonzero imaginary coefficient. The real and imaginary outputs carry different information.
• A radian angle looks wrong: multiply the imaginary coefficient by LN(2), or use IMARGUMENT directly.
• The input is zero: a complex logarithm of zero is not finite. The cited entry does not assign a verified function-specific error token for that case.
• Negative-real-axis or branch-boundary input: the short help entry does not give a complete branch convention. These worked cases avoid that boundary; do not generalize a single logarithm identity across it without checking the intended environment.
• Formula or text is rejected: check lowercase suffix, literal quotes, the referenced value and the local decimal convention. Zoho’s general error list is not an exhaustive mapping for malformed complex strings.
• Imported results differ slightly: compare numeric coefficients with a tolerance appropriate to the calculation, rather than demanding character-for-character equality of complex output text.

Keep the original input alongside the result and do not round its coefficients prematurely. This makes the magnitude, angle and base-conversion checks reproducible.