Rewrite in Standard Form (3+5i)/(6- square root of 2i)*(6+ square root of 2i)/(6+ square root of 2i)

Math
3+5i6-2i⋅6+2i6+2i
Multiply the numerator and denominator of 3+5i6-1.41421356i by the conjugate of 6-1.41421356i to make the denominator real.
3+5i6-1.41421356i⋅6+1.41421356i6+1.41421356i⋅6+2i6+2i
Multiply.
Tap for more steps…
Combine.
(3+5i)(6+1.41421356i)(6-1.41421356i)(6+1.41421356i)⋅6+2i6+2i
Simplify the numerator.
Tap for more steps…
Expand (3+5i)(6+1.41421356i) using the FOIL Method.
Tap for more steps…
Apply the distributive property.
3(6+1.41421356i)+5i(6+1.41421356i)(6-1.41421356i)(6+1.41421356i)⋅6+2i6+2i
Apply the distributive property.
3⋅6+3(1.41421356i)+5i(6+1.41421356i)(6-1.41421356i)(6+1.41421356i)⋅6+2i6+2i
Apply the distributive property.
3⋅6+3(1.41421356i)+5i⋅6+5i(1.41421356i)(6-1.41421356i)(6+1.41421356i)⋅6+2i6+2i
3⋅6+3(1.41421356i)+5i⋅6+5i(1.41421356i)(6-1.41421356i)(6+1.41421356i)⋅6+2i6+2i
Simplify and combine like terms.
Tap for more steps…
Simplify each term.
Tap for more steps…
Multiply 3 by 6.
18+3(1.41421356i)+5i⋅6+5i(1.41421356i)(6-1.41421356i)(6+1.41421356i)⋅6+2i6+2i
Multiply 1.41421356 by 3.
18+4.24264068i+5i⋅6+5i(1.41421356i)(6-1.41421356i)(6+1.41421356i)⋅6+2i6+2i
Multiply 6 by 5.
18+4.24264068i+30i+5i(1.41421356i)(6-1.41421356i)(6+1.41421356i)⋅6+2i6+2i
Multiply 5i(1.41421356i).
Tap for more steps…
Multiply 1.41421356 by 5.
18+4.24264068i+30i+7.07106781ii(6-1.41421356i)(6+1.41421356i)⋅6+2i6+2i
Raise i to the power of 1.
18+4.24264068i+30i+7.07106781(i1i)(6-1.41421356i)(6+1.41421356i)⋅6+2i6+2i
Raise i to the power of 1.
18+4.24264068i+30i+7.07106781(i1i1)(6-1.41421356i)(6+1.41421356i)⋅6+2i6+2i
Use the power rule aman=am+n to combine exponents.
18+4.24264068i+30i+7.07106781i1+1(6-1.41421356i)(6+1.41421356i)⋅6+2i6+2i
Add 1 and 1.
18+4.24264068i+30i+7.07106781i2(6-1.41421356i)(6+1.41421356i)⋅6+2i6+2i
18+4.24264068i+30i+7.07106781i2(6-1.41421356i)(6+1.41421356i)⋅6+2i6+2i
Rewrite i2 as -1.
18+4.24264068i+30i+7.07106781⋅-1(6-1.41421356i)(6+1.41421356i)⋅6+2i6+2i
Multiply 7.07106781 by -1.
18+4.24264068i+30i-7.07106781(6-1.41421356i)(6+1.41421356i)⋅6+2i6+2i
18+4.24264068i+30i-7.07106781(6-1.41421356i)(6+1.41421356i)⋅6+2i6+2i
Subtract 7.07106781 from 18.
10.92893218+4.24264068i+30i(6-1.41421356i)(6+1.41421356i)⋅6+2i6+2i
Add 4.24264068i and 30i.
10.92893218+34.24264068i(6-1.41421356i)(6+1.41421356i)⋅6+2i6+2i
10.92893218+34.24264068i(6-1.41421356i)(6+1.41421356i)⋅6+2i6+2i
10.92893218+34.24264068i(6-1.41421356i)(6+1.41421356i)⋅6+2i6+2i
Simplify the denominator.
Tap for more steps…
Expand (6-1.41421356i)(6+1.41421356i) using the FOIL Method.
Tap for more steps…
Apply the distributive property.
10.92893218+34.24264068i6(6+1.41421356i)-1.41421356i(6+1.41421356i)⋅6+2i6+2i
Apply the distributive property.
10.92893218+34.24264068i6⋅6+6(1.41421356i)-1.41421356i(6+1.41421356i)⋅6+2i6+2i
Apply the distributive property.
10.92893218+34.24264068i6⋅6+6(1.41421356i)-1.41421356i⋅6-1.41421356i(1.41421356i)⋅6+2i6+2i
10.92893218+34.24264068i6⋅6+6(1.41421356i)-1.41421356i⋅6-1.41421356i(1.41421356i)⋅6+2i6+2i
Simplify.
Tap for more steps…
Multiply 6 by 6.
10.92893218+34.24264068i36+6(1.41421356i)-1.41421356i⋅6-1.41421356i(1.41421356i)⋅6+2i6+2i
Multiply 1.41421356 by 6.
10.92893218+34.24264068i36+8.48528137i-1.41421356i⋅6-1.41421356i(1.41421356i)⋅6+2i6+2i
Multiply 6 by -1.41421356.
10.92893218+34.24264068i36+8.48528137i-8.48528137i-1.41421356i(1.41421356i)⋅6+2i6+2i
Multiply 1.41421356 by -1.41421356.
10.92893218+34.24264068i36+8.48528137i-8.48528137i-2ii⋅6+2i6+2i
Raise i to the power of 1.
10.92893218+34.24264068i36+8.48528137i-8.48528137i-2(i1i)⋅6+2i6+2i
Raise i to the power of 1.
10.92893218+34.24264068i36+8.48528137i-8.48528137i-2(i1i1)⋅6+2i6+2i
Use the power rule aman=am+n to combine exponents.
10.92893218+34.24264068i36+8.48528137i-8.48528137i-2i1+1⋅6+2i6+2i
Add 1 and 1.
10.92893218+34.24264068i36+8.48528137i-8.48528137i-2i2⋅6+2i6+2i
Subtract 8.48528137i from 8.48528137i.
10.92893218+34.24264068i36+0i-2i2⋅6+2i6+2i
10.92893218+34.24264068i36+0i-2i2⋅6+2i6+2i
Simplify each term.
Tap for more steps…
Multiply 0 by i.
10.92893218+34.24264068i36+0-2i2⋅6+2i6+2i
Rewrite i2 as -1.
10.92893218+34.24264068i36+0-2⋅-1⋅6+2i6+2i
Multiply -2 by -1.
10.92893218+34.24264068i36+0+2⋅6+2i6+2i
10.92893218+34.24264068i36+0+2⋅6+2i6+2i
Add 36 and 0.
10.92893218+34.24264068i36+2⋅6+2i6+2i
Add 36 and 2.
10.92893218+34.24264068i38⋅6+2i6+2i
10.92893218+34.24264068i38⋅6+2i6+2i
10.92893218+34.24264068i38⋅6+2i6+2i
Rewrite 10.92893218 as 1(10.92893218).
1(10.92893218)+34.24264068i38⋅6+2i6+2i
Factor 1 out of 34.24264068i.
1(10.92893218)+1(34.24264068i)38⋅6+2i6+2i
Factor 1 out of 1(10.92893218)+1(34.24264068i).
1(10.92893218+34.24264068i)38⋅6+2i6+2i
Factor 38 out of 38.
1(10.92893218+34.24264068i)38(1)⋅6+2i6+2i
Separate fractions.
138⋅10.92893218+34.24264068i1⋅6+2i6+2i
Divide 1 by 38.
0.0263157810.92893218+34.24264068i1⋅6+2i6+2i
Divide 10.92893218+34.24264068i by 1.
0.02631578(10.92893218+34.24264068i)⋅6+2i6+2i
Apply the distributive property.
(0.02631578⋅10.92893218+0.02631578(34.24264068i))⋅6+2i6+2i
Multiply 0.02631578 by 10.92893218.
(0.28760347+0.02631578(34.24264068i))⋅6+2i6+2i
Multiply 34.24264068 by 0.02631578.
(0.28760347+0.90112212i)⋅6+2i6+2i
Cancel the common factor of 6+2i.
Tap for more steps…
Cancel the common factor.
(0.28760347+0.90112212i)⋅6+2i6+2i
Divide 1 by 1.
(0.28760347+0.90112212i)⋅1
(0.28760347+0.90112212i)⋅1
Multiply 0.28760347+0.90112212i by 1.
0.28760347+0.90112212i
Rewrite in Standard Form (3+5i)/(6- square root of 2i)*(6+ square root of 2i)/(6+ square root of 2i)

Meet the Team our Math Expers

Our Professionals

Robert Kristofer

Anna Frok

Magnus Flores

Lydia Fran

We are MathExperts

Solve all your Math Problems: https://elanyachtselection.com/

We can solve all your math problems
Scroll to top