Basic Math Examples

Write in Standard Form (6i)/(5-4i)
6i5-4i
Step 1
Multiply the numerator and denominator of 6i5-4i by the conjugate of 5-4i to make the denominator real.
6i5-4i5+4i5+4i
Step 2
Multiply.
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Step 2.1
Combine.
6i(5+4i)(5-4i)(5+4i)
Step 2.2
Simplify the numerator.
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Step 2.2.1
Apply the distributive property.
6i5+6i(4i)(5-4i)(5+4i)
Step 2.2.2
Multiply 5 by 6.
30i+6i(4i)(5-4i)(5+4i)
Step 2.2.3
Multiply 6i(4i).
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Step 2.2.3.1
Multiply 4 by 6.
30i+24ii(5-4i)(5+4i)
Step 2.2.3.2
Raise i to the power of 1.
30i+24(i1i)(5-4i)(5+4i)
Step 2.2.3.3
Raise i to the power of 1.
30i+24(i1i1)(5-4i)(5+4i)
Step 2.2.3.4
Use the power rule aman=am+n to combine exponents.
30i+24i1+1(5-4i)(5+4i)
Step 2.2.3.5
Add 1 and 1.
30i+24i2(5-4i)(5+4i)
30i+24i2(5-4i)(5+4i)
Step 2.2.4
Simplify each term.
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Step 2.2.4.1
Rewrite i2 as -1.
30i+24-1(5-4i)(5+4i)
Step 2.2.4.2
Multiply 24 by -1.
30i-24(5-4i)(5+4i)
30i-24(5-4i)(5+4i)
Step 2.2.5
Reorder 30i and -24.
-24+30i(5-4i)(5+4i)
-24+30i(5-4i)(5+4i)
Step 2.3
Simplify the denominator.
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Step 2.3.1
Expand (5-4i)(5+4i) using the FOIL Method.
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Step 2.3.1.1
Apply the distributive property.
-24+30i5(5+4i)-4i(5+4i)
Step 2.3.1.2
Apply the distributive property.
-24+30i55+5(4i)-4i(5+4i)
Step 2.3.1.3
Apply the distributive property.
-24+30i55+5(4i)-4i5-4i(4i)
-24+30i55+5(4i)-4i5-4i(4i)
Step 2.3.2
Simplify.
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Step 2.3.2.1
Multiply 5 by 5.
-24+30i25+5(4i)-4i5-4i(4i)
Step 2.3.2.2
Multiply 4 by 5.
-24+30i25+20i-4i5-4i(4i)
Step 2.3.2.3
Multiply 5 by -4.
-24+30i25+20i-20i-4i(4i)
Step 2.3.2.4
Multiply 4 by -4.
-24+30i25+20i-20i-16ii
Step 2.3.2.5
Raise i to the power of 1.
-24+30i25+20i-20i-16(i1i)
Step 2.3.2.6
Raise i to the power of 1.
-24+30i25+20i-20i-16(i1i1)
Step 2.3.2.7
Use the power rule aman=am+n to combine exponents.
-24+30i25+20i-20i-16i1+1
Step 2.3.2.8
Add 1 and 1.
-24+30i25+20i-20i-16i2
Step 2.3.2.9
Subtract 20i from 20i.
-24+30i25+0-16i2
Step 2.3.2.10
Add 25 and 0.
-24+30i25-16i2
-24+30i25-16i2
Step 2.3.3
Simplify each term.
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Step 2.3.3.1
Rewrite i2 as -1.
-24+30i25-16-1
Step 2.3.3.2
Multiply -16 by -1.
-24+30i25+16
-24+30i25+16
Step 2.3.4
Add 25 and 16.
-24+30i41
-24+30i41
-24+30i41
Step 3
Split the fraction -24+30i41 into two fractions.
-2441+30i41
Step 4
Move the negative in front of the fraction.
-2441+30i41
 [x2  12  π  xdx ]