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Basic Math Examples
-8-6i-10+2i−8−6i−10+2i
Step 1
Step 1.1
Factor 22 out of -8−8.
2⋅-4-6i-10+2i2⋅−4−6i−10+2i
Step 1.2
Factor 22 out of -6i−6i.
2⋅-4+2(-3i)-10+2i2⋅−4+2(−3i)−10+2i
Step 1.3
Factor 22 out of 2(-4)+2(-3i)2(−4)+2(−3i).
2(-4-3i)-10+2i2(−4−3i)−10+2i
Step 1.4
Cancel the common factors.
Step 1.4.1
Factor 22 out of -10−10.
2(-4-3i)2(-5)+2i2(−4−3i)2(−5)+2i
Step 1.4.2
Factor 22 out of 2i2i.
2(-4-3i)2(-5)+2(i)2(−4−3i)2(−5)+2(i)
Step 1.4.3
Factor 22 out of 2(-5)+2(i)2(−5)+2(i).
2(-4-3i)2(-5+i)2(−4−3i)2(−5+i)
Step 1.4.4
Cancel the common factor.
2(-4-3i)2(-5+i)
Step 1.4.5
Rewrite the expression.
-4-3i-5+i
-4-3i-5+i
-4-3i-5+i
Step 2
Multiply the numerator and denominator of -4-3i-5+1i by the conjugate of -5+1i to make the denominator real.
-4-3i-5+1i⋅-5-i-5-i
Step 3
Step 3.1
Combine.
(-4-3i)(-5-i)(-5+1i)(-5-i)
Step 3.2
Simplify the numerator.
Step 3.2.1
Expand (-4-3i)(-5-i) using the FOIL Method.
Step 3.2.1.1
Apply the distributive property.
-4(-5-i)-3i(-5-i)(-5+1i)(-5-i)
Step 3.2.1.2
Apply the distributive property.
-4⋅-5-4(-i)-3i(-5-i)(-5+1i)(-5-i)
Step 3.2.1.3
Apply the distributive property.
-4⋅-5-4(-i)-3i⋅-5-3i(-i)(-5+1i)(-5-i)
-4⋅-5-4(-i)-3i⋅-5-3i(-i)(-5+1i)(-5-i)
Step 3.2.2
Simplify and combine like terms.
Step 3.2.2.1
Simplify each term.
Step 3.2.2.1.1
Multiply -4 by -5.
20-4(-i)-3i⋅-5-3i(-i)(-5+1i)(-5-i)
Step 3.2.2.1.2
Multiply -1 by -4.
20+4i-3i⋅-5-3i(-i)(-5+1i)(-5-i)
Step 3.2.2.1.3
Multiply -5 by -3.
20+4i+15i-3i(-i)(-5+1i)(-5-i)
Step 3.2.2.1.4
Multiply -3i(-i).
Step 3.2.2.1.4.1
Multiply -1 by -3.
20+4i+15i+3ii(-5+1i)(-5-i)
Step 3.2.2.1.4.2
Raise i to the power of 1.
20+4i+15i+3(i1i)(-5+1i)(-5-i)
Step 3.2.2.1.4.3
Raise i to the power of 1.
20+4i+15i+3(i1i1)(-5+1i)(-5-i)
Step 3.2.2.1.4.4
Use the power rule aman=am+n to combine exponents.
20+4i+15i+3i1+1(-5+1i)(-5-i)
Step 3.2.2.1.4.5
Add 1 and 1.
20+4i+15i+3i2(-5+1i)(-5-i)
20+4i+15i+3i2(-5+1i)(-5-i)
Step 3.2.2.1.5
Rewrite i2 as -1.
20+4i+15i+3⋅-1(-5+1i)(-5-i)
Step 3.2.2.1.6
Multiply 3 by -1.
20+4i+15i-3(-5+1i)(-5-i)
20+4i+15i-3(-5+1i)(-5-i)
Step 3.2.2.2
Subtract 3 from 20.
17+4i+15i(-5+1i)(-5-i)
Step 3.2.2.3
Add 4i and 15i.
17+19i(-5+1i)(-5-i)
17+19i(-5+1i)(-5-i)
17+19i(-5+1i)(-5-i)
Step 3.3
Simplify the denominator.
Step 3.3.1
Expand (-5+1i)(-5-i) using the FOIL Method.
Step 3.3.1.1
Apply the distributive property.
17+19i-5(-5-i)+1i(-5-i)
Step 3.3.1.2
Apply the distributive property.
17+19i-5⋅-5-5(-i)+1i(-5-i)
Step 3.3.1.3
Apply the distributive property.
17+19i-5⋅-5-5(-i)+1i⋅-5+1i(-i)
17+19i-5⋅-5-5(-i)+1i⋅-5+1i(-i)
Step 3.3.2
Simplify.
Step 3.3.2.1
Multiply -5 by -5.
17+19i25-5(-i)+1i⋅-5+1i(-i)
Step 3.3.2.2
Multiply -1 by -5.
17+19i25+5i+1i⋅-5+1i(-i)
Step 3.3.2.3
Multiply -5 by 1.
17+19i25+5i-5i+1i(-i)
Step 3.3.2.4
Multiply -1 by 1.
17+19i25+5i-5i-ii
Step 3.3.2.5
Raise i to the power of 1.
17+19i25+5i-5i-(i1i)
Step 3.3.2.6
Raise i to the power of 1.
17+19i25+5i-5i-(i1i1)
Step 3.3.2.7
Use the power rule aman=am+n to combine exponents.
17+19i25+5i-5i-i1+1
Step 3.3.2.8
Add 1 and 1.
17+19i25+5i-5i-i2
Step 3.3.2.9
Subtract 5i from 5i.
17+19i25+0-i2
Step 3.3.2.10
Add 25 and 0.
17+19i25-i2
17+19i25-i2
Step 3.3.3
Simplify each term.
Step 3.3.3.1
Rewrite i2 as -1.
17+19i25--1
Step 3.3.3.2
Multiply -1 by -1.
17+19i25+1
17+19i25+1
Step 3.3.4
Add 25 and 1.
17+19i26
17+19i26
17+19i26
Step 4
Split the fraction 17+19i26 into two fractions.
1726+19i26