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How to Solve Rationalizing Imaginary Denominators? (+FREE Worksheet!)

The following step-by-step guide helps you learn how to rationalize imaginary denominators. 

How to Solve Rationalizing Imaginary Denominators? (+FREE Worksheet!)

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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: 23i6i

Solution:

Multiply by the conjugate: ii:
23i6i=(23i)(i)6i(i)=32i6=1213i

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Rationalizing Imaginary Denominators – Example 2:

Solve: 8i24i

Solution:

Factor 24i=2(12i), then: 8i2(12i)=4i(12i)
Multiply by the conjugate 1+2i1+2i:

4i12i=4i(1+2i)(12i)(1+2i)=8+4i5=85+45i

Rationalizing Imaginary Denominators – Example 3:

Solve: 5i23i

Solution:

Multiply by the conjugate: 2+3i2+3i:

5i23i=5i(2+3i)(23i)(2+3i)=15+10i(23i)(2+3i)
Use complex arithmetic rule: (a+bi)(abi)=a2+b2
(23i)(2+3i)=22+(3)2=4+9=13 ,

Then: 15+10i(23i)(2+3i)=15+10i13=1513+1013i

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Rationalizing Imaginary Denominators – Example 4:

Solve: 49i6i

Solution:

Apply fraction rule: 49i6i=49i6i
Multiply by the conjugate: ii.
49i6i=(49i)(i)6i(i)=94i6=32+23i

Exercises for Solving Rationalizing Imaginary Denominators

Simplify.

  • 1010i5i 
  • 58i10i 
  • 6+8i9i 
  • 8i1+3i 
  • 5i26i 
  • 105i6+6i 

Download Rationalizing Imaginary Denominators Worksheet

  • 2+2i 
  • 45+12i 
  • 8923i 
  • 12545i 
  • 3414i 
  • 512+54i 

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Original price was: $29.99.Current price is: $19.99.
Original price was: $29.99.Current price is: $19.99.
Original price was: $29.99.Current price is: $19.99.

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