Dividing

Simplify 3i/-2

3/2i x i/i

Because i is a radical, this fraction is not simplified.

To rationalize the denominator, we will multiply the denominator and numerator by i. Remember, this is really multiplying by 1.

3i/2i squared

Remember i2 = 1

3i/-2

Simplify 1-i / 2+i

To remove the radical from the denominator here, we use the conjugate just like we did with irrational radicals.

The conjugate is the exact same terms with the opposite sign in between.

The conjugate of 8 - i is 8 + i.

The congugate of -11 + 6i is -11 - 6i.

The conjugate of our denominator is 2 - i.

1-i / 2 + i

1-i / 2 + i + blank

Multiply by the conjugate in the form of a 1.

Answer: 1-i / 2 + i + 2-i / 2-i

Use binomial multiplication in numerator and denominator.

___(2-i) + (___)(2-i)/___(2+i) + ___(2+i)

Answer: 1(2-i) + (-i)(2-i) / 2(2+i) + i(2+i)

Now simplify.

2 - i - 2 ___ + isup2 / ___ - ___ + 2i - isup2

Answer: 2 - i - 2i + isup2 / 4 - 2i + 2i - isup2

2 - i - 2i + isup2 / 4 - 2i + 2i - isup2 = 2 - ___ - ___ / ___ + ___

Answer: 2 - 3i - 1 / 4 + 1

2 - i - 2i + isup2 / 4 - 2i + 2i - isup2 = 2 - 3i - 1 / 4 + 1 = ___ / ___

Answer: 1 - 3i / 5

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