Write in Standard Form (4+5i)/(2+7i)

Math
4+5i2+7i
Multiply the numerator and denominator of 4+5i2+7i by the conjugate of 2+7i to make the denominator real.
4+5i2+7i⋅2-7i2-7i
Multiply.
Tap for more steps…
Combine.
(4+5i)(2-7i)(2+7i)(2-7i)
Simplify the numerator.
Tap for more steps…
Expand (4+5i)(2-7i) using the FOIL Method.
Tap for more steps…
Apply the distributive property.
4(2-7i)+5i(2-7i)(2+7i)(2-7i)
Apply the distributive property.
4⋅2+4(-7i)+5i(2-7i)(2+7i)(2-7i)
Apply the distributive property.
4⋅2+4(-7i)+5i⋅2+5i(-7i)(2+7i)(2-7i)
4⋅2+4(-7i)+5i⋅2+5i(-7i)(2+7i)(2-7i)
Simplify and combine like terms.
Tap for more steps…
Simplify each term.
Tap for more steps…
Multiply 4 by 2.
8+4(-7i)+5i⋅2+5i(-7i)(2+7i)(2-7i)
Multiply -7 by 4.
8-28i+5i⋅2+5i(-7i)(2+7i)(2-7i)
Multiply 2 by 5.
8-28i+10i+5i(-7i)(2+7i)(2-7i)
Multiply 5i(-7i).
Tap for more steps…
Multiply -7 by 5.
8-28i+10i-35ii(2+7i)(2-7i)
Raise i to the power of 1.
8-28i+10i-35(i1i)(2+7i)(2-7i)
Raise i to the power of 1.
8-28i+10i-35(i1i1)(2+7i)(2-7i)
Use the power rule aman=am+n to combine exponents.
8-28i+10i-35i1+1(2+7i)(2-7i)
Add 1 and 1.
8-28i+10i-35i2(2+7i)(2-7i)
8-28i+10i-35i2(2+7i)(2-7i)
Rewrite i2 as -1.
8-28i+10i-35⋅-1(2+7i)(2-7i)
Multiply -35 by -1.
8-28i+10i+35(2+7i)(2-7i)
8-28i+10i+35(2+7i)(2-7i)
Add 8 and 35.
43-28i+10i(2+7i)(2-7i)
Add -28i and 10i.
43-18i(2+7i)(2-7i)
43-18i(2+7i)(2-7i)
43-18i(2+7i)(2-7i)
Simplify the denominator.
Tap for more steps…
Expand (2+7i)(2-7i) using the FOIL Method.
Tap for more steps…
Apply the distributive property.
43-18i2(2-7i)+7i(2-7i)
Apply the distributive property.
43-18i2⋅2+2(-7i)+7i(2-7i)
Apply the distributive property.
43-18i2⋅2+2(-7i)+7i⋅2+7i(-7i)
43-18i2⋅2+2(-7i)+7i⋅2+7i(-7i)
Simplify.
Tap for more steps…
Multiply 2 by 2.
43-18i4+2(-7i)+7i⋅2+7i(-7i)
Multiply -7 by 2.
43-18i4-14i+7i⋅2+7i(-7i)
Multiply 2 by 7.
43-18i4-14i+14i+7i(-7i)
Multiply -7 by 7.
43-18i4-14i+14i-49ii
Raise i to the power of 1.
43-18i4-14i+14i-49(i1i)
Raise i to the power of 1.
43-18i4-14i+14i-49(i1i1)
Use the power rule aman=am+n to combine exponents.
43-18i4-14i+14i-49i1+1
Add 1 and 1.
43-18i4-14i+14i-49i2
Add -14i and 14i.
43-18i4+0-49i2
Add 4 and 0.
43-18i4-49i2
43-18i4-49i2
Simplify each term.
Tap for more steps…
Rewrite i2 as -1.
43-18i4-49⋅-1
Multiply -49 by -1.
43-18i4+49
43-18i4+49
Add 4 and 49.
43-18i53
43-18i53
43-18i53
Split the fraction 43-18i53 into two fractions.
4353+-18i53
Move the negative in front of the fraction.
4353-18i53
Write in Standard Form (4+5i)/(2+7i)

Solving MATH problems

We can solve all math problems. Get help on the web or with our math app

Scroll to top