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Basic Math Examples
11-6i8i11−6i8i
Step 1
Multiply the numerator and denominator of 11-6i8i11−6i8i by the conjugate of 8i8i to make the denominator real.
11-6i8i⋅ii11−6i8i⋅ii
Step 2
Step 2.1
Combine.
(11-6i)i8ii(11−6i)i8ii
Step 2.2
Simplify the numerator.
Step 2.2.1
Apply the distributive property.
11i-6ii8ii11i−6ii8ii
Step 2.2.2
Multiply -6ii−6ii.
Step 2.2.2.1
Raise ii to the power of 11.
11i-6(i1i)8ii11i−6(i1i)8ii
Step 2.2.2.2
Raise ii to the power of 11.
11i-6(i1i1)8ii11i−6(i1i1)8ii
Step 2.2.2.3
Use the power rule aman=am+naman=am+n to combine exponents.
11i-6i1+18ii11i−6i1+18ii
Step 2.2.2.4
Add 11 and 11.
11i-6i28ii11i−6i28ii
11i-6i28ii11i−6i28ii
Step 2.2.3
Simplify each term.
Step 2.2.3.1
Rewrite i2i2 as -1−1.
11i-6⋅-18ii11i−6⋅−18ii
Step 2.2.3.2
Multiply -6−6 by -1−1.
11i+68ii11i+68ii
11i+68ii11i+68ii
Step 2.2.4
Reorder 11i11i and 66.
6+11i8ii6+11i8ii
6+11i8ii6+11i8ii
Step 2.3
Simplify the denominator.
Step 2.3.1
Add parentheses.
6+11i8(ii)6+11i8(ii)
Step 2.3.2
Raise ii to the power of 11.
6+11i8(i1i)6+11i8(i1i)
Step 2.3.3
Raise ii to the power of 11.
6+11i8(i1i1)6+11i8(i1i1)
Step 2.3.4
Use the power rule aman=am+naman=am+n to combine exponents.
6+11i8i1+16+11i8i1+1
Step 2.3.5
Add 11 and 11.
6+11i8i26+11i8i2
Step 2.3.6
Rewrite i2i2 as -1−1.
6+11i8⋅-16+11i8⋅−1
6+11i8⋅-16+11i8⋅−1
6+11i8⋅-16+11i8⋅−1
Step 3
Multiply 88 by -1−1.
6+11i-86+11i−8
Step 4
Split the fraction 6+11i-86+11i−8 into two fractions.
6-8+11i-86−8+11i−8
Step 5
Step 5.1
Cancel the common factor of 66 and -8−8.
Step 5.1.1
Factor 22 out of 66.
2(3)-8+11i-82(3)−8+11i−8
Step 5.1.2
Cancel the common factors.
Step 5.1.2.1
Factor 22 out of -8−8.
2⋅32⋅-4+11i-82⋅32⋅−4+11i−8
Step 5.1.2.2
Cancel the common factor.
2⋅32⋅-4+11i-8
Step 5.1.2.3
Rewrite the expression.
3-4+11i-8
3-4+11i-8
3-4+11i-8
Step 5.2
Move the negative in front of the fraction.
-34+11i-8
Step 5.3
Move the negative in front of the fraction.
-34-11i8
-34-11i8