How to Solve Rationalizing Imaginary Denominators? (+FREE Worksheet!)
The following step-by-step guide helps you learn how to rationalize imaginary denominators.

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Step by step guide to rationalizing Imaginary Denominators
- Step 1: Find the conjugate (it’s the denominator with different sign between the two terms.
- Step 2: Multiply the numerator and denominator by the conjugate.
- Step 3: Simplify if needed.
Rationalizing Imaginary Denominators – Example 1:
Solve: 2−3i6i
Solution:
Multiply by the conjugate: −i−i:
2−3i6i=(2−3i)(−i)6i(−i)=−3−2i6=−12−13i
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Rationalizing Imaginary Denominators – Example 2:
Solve: 8i2–4i
Solution:
Factor 2–4i=2(1−2i), then: 8i2(1−2i)=4i(1−2i)
Multiply by the conjugate 1+2i1+2i:
4i1−2i=4i(1+2i)(1−2i)(1+2i)=−8+4i5=−85+45i
Rationalizing Imaginary Denominators – Example 3:
Solve: 5i2–3i
Solution:
Multiply by the conjugate: 2+3i2+3i:
5i2–3i=5i(2+3i)(2−3i)(2+3i)=−15+10i(2−3i)(2+3i)
Use complex arithmetic rule: (a+bi)(a−bi)=a2+b2
(2−3i)(2+3i)=−22+(−3)2=4+9=13 ,
Then: −15+10i(2−3i)(2+3i)=−15+10i13=−1513+1013i
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Rationalizing Imaginary Denominators – Example 4:
Solve: 4−9i−6i
Solution:
Apply fraction rule: 4−9i−6i=−4−9i6i
Multiply by the conjugate: −i−i.
−4−9i6i=−(4−9i)(−i)6i(−i)=−−9−4i6=32+23i
Exercises for Solving Rationalizing Imaginary Denominators
Simplify.
- 10–10i−5i
- 5–8i−10i
- 6+8i9i
- 8i−1+3i
- 5i−2–6i
- −10–5i−6+6i
Download Rationalizing Imaginary Denominators Worksheet

- 2+2i
- 45+12i
- 89−23i
- 125−45i
- −34−14i
- 512+54i
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