To divide complex numbers, create the problem in fraction type first. Indigenous there, it will certainly be straightforward to figure out what to perform next. Another step is to find the conjugate the the denominator. Just in instance you forgot exactly how to identify the conjugate that a given facility number, see the table below:

Conjugate that a complex Number


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Use this conjugate to main point the numerator and also denominator the the given trouble then simplify. You might need to discover or testimonial the ability on exactly how to multiply facility numbers because it will play an essential role in dividing facility numbers.

You are watching: Divide and simplify to the form a bi

You will observe later on that the product of a facility number with its conjugate will always yield a actual number. The imaginary component dropsfrom the process because lock cancel each other.

It is much much easier than the sounds. Below are part examples!

Examples of just how to Divide complex Numbers


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Since ours denominator is 1 + 2i, its conjugateis equal to 1 - 2i. Psychic to adjust only the sign of the imagine term to obtain the conjugate.

We take it this conjugate and use it as the typical multiplier the both the numerator and also denominator.


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From here, we just need to main point the molecule together and also the denominators as well. Usage the FOIL technique when multiply the binomials. Execute all vital simplifications to get the final answer.

Don’t forget to use the truth that i^2 = - 1.


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Since the denominator is - \,3 - i,its conjugate equals - \,3 + i. main point the top and also bottom that the fraction by this conjugate.

Towards the finish of the simplification, publication the common factor of the numerator and also denominator. In this process, the common factor is 5.


The problem is currently in the form that us want, that is, in fountain form. The conjugate the the denominator - \,5 + 5i is - 5 - 5i.

Let’s multiply the numerator and denominator through this conjugate, and also simplify.

See more: How To Cube Root On A Ti-84 Plus, How To Find Cube Root In Ti


Since the denominator is 1 + i, that conjugate need to be 1 - i. Multiply the top and also bottom of the portion by this conjugateand simplify.


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