Where's the denominator

Mathematics

ScanSolve AI Answer

Answer

41

Step 4: Multiply the denominators.
We are multiplying (−4−5i)(-4-5i) by its conjugate (−4+5i)(-4+5i). This follows the form (a−bi)(a+bi)=a2+b2(a-bi)(a+bi) = a^2 + b^2.
Here, a=−4a=-4 and b=5b=5.

(−4−5i)(−4+5i)=(−4)2−(5i)2(-4-5i)(-4+5i) = (-4)^2 - (5i)^2 =16−(25i2)= 16 - (25i^2)

Substitute i2=−1i^2 = -1:

=16−25(−1)= 16 - 25(-1) =16+25= 16 + 25 =41= 41

The denominator is 41.

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