Write in Standard Form (9+3i)/(7+2i)

Math
9+3i7+2i
Multiply the numerator and denominator of 9+3i7+2i by the conjugate of 7+2i to make the denominator real.
9+3i7+2i⋅7-2i7-2i
Multiply.
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Combine.
(9+3i)(7-2i)(7+2i)(7-2i)
Simplify the numerator.
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Expand (9+3i)(7-2i) using the FOIL Method.
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Apply the distributive property.
9(7-2i)+3i(7-2i)(7+2i)(7-2i)
Apply the distributive property.
9⋅7+9(-2i)+3i(7-2i)(7+2i)(7-2i)
Apply the distributive property.
9⋅7+9(-2i)+3i⋅7+3i(-2i)(7+2i)(7-2i)
9⋅7+9(-2i)+3i⋅7+3i(-2i)(7+2i)(7-2i)
Simplify and combine like terms.
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Simplify each term.
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Multiply 9 by 7.
63+9(-2i)+3i⋅7+3i(-2i)(7+2i)(7-2i)
Multiply -2 by 9.
63-18i+3i⋅7+3i(-2i)(7+2i)(7-2i)
Multiply 7 by 3.
63-18i+21i+3i(-2i)(7+2i)(7-2i)
Multiply 3i(-2i).
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Multiply -2 by 3.
63-18i+21i-6ii(7+2i)(7-2i)
Raise i to the power of 1.
63-18i+21i-6(i1i)(7+2i)(7-2i)
Raise i to the power of 1.
63-18i+21i-6(i1i1)(7+2i)(7-2i)
Use the power rule aman=am+n to combine exponents.
63-18i+21i-6i1+1(7+2i)(7-2i)
Add 1 and 1.
63-18i+21i-6i2(7+2i)(7-2i)
63-18i+21i-6i2(7+2i)(7-2i)
Rewrite i2 as -1.
63-18i+21i-6⋅-1(7+2i)(7-2i)
Multiply -6 by -1.
63-18i+21i+6(7+2i)(7-2i)
63-18i+21i+6(7+2i)(7-2i)
Add 63 and 6.
69-18i+21i(7+2i)(7-2i)
Add -18i and 21i.
69+3i(7+2i)(7-2i)
69+3i(7+2i)(7-2i)
69+3i(7+2i)(7-2i)
Simplify the denominator.
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Expand (7+2i)(7-2i) using the FOIL Method.
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Apply the distributive property.
69+3i7(7-2i)+2i(7-2i)
Apply the distributive property.
69+3i7⋅7+7(-2i)+2i(7-2i)
Apply the distributive property.
69+3i7⋅7+7(-2i)+2i⋅7+2i(-2i)
69+3i7⋅7+7(-2i)+2i⋅7+2i(-2i)
Simplify.
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Multiply 7 by 7.
69+3i49+7(-2i)+2i⋅7+2i(-2i)
Multiply -2 by 7.
69+3i49-14i+2i⋅7+2i(-2i)
Multiply 7 by 2.
69+3i49-14i+14i+2i(-2i)
Multiply -2 by 2.
69+3i49-14i+14i-4ii
Raise i to the power of 1.
69+3i49-14i+14i-4(i1i)
Raise i to the power of 1.
69+3i49-14i+14i-4(i1i1)
Use the power rule aman=am+n to combine exponents.
69+3i49-14i+14i-4i1+1
Add 1 and 1.
69+3i49-14i+14i-4i2
Add -14i and 14i.
69+3i49+0-4i2
Add 49 and 0.
69+3i49-4i2
69+3i49-4i2
Simplify each term.
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Rewrite i2 as -1.
69+3i49-4⋅-1
Multiply -4 by -1.
69+3i49+4
69+3i49+4
Add 49 and 4.
69+3i53
69+3i53
69+3i53
Split the fraction 69+3i53 into two fractions.
6953+3i53
Write in Standard Form (9+3i)/(7+2i)

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