Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Multiply and simplify the following complex numbers: (-3-i)*(3+i)

Multiply and simplify the following complex numbers:\newline(−3−i)⋅(3+i) (-3-i) \cdot(3+i)

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Grade 8right chevron icon
Multiply numbers written in scientific notationright chevron icon

Full solution

Q. Multiply and simplify the following complex numbers:\newline(−3−i)⋅(3+i) (-3-i) \cdot(3+i)
  1. Apply distributive property: Apply the distributive property (also known as the FOIL method for binomials) to multiply the two complex numbers.\newline(−3−i)∗(3+i)=(−3)∗(3)+(−3)∗(i)+(−i)∗(3)+(−i)∗(i)(-3-i)*(3+i) = (-3)*(3) + (-3)*(i) + (-i)*(3) + (-i)*(i)
  2. Multiply terms: Multiply each term.\newline(−3)⋅(3)=−9(-3)\cdot(3) = -9\newline(−3)⋅(i)=−3i(-3)\cdot(i) = -3i\newline(−i)⋅(3)=−3i(-i)\cdot(3) = -3i\newline(−i)⋅(i)=−i2(-i)\cdot(i) = -i^2
  3. Evaluate i2i^2: Remember that i2i^2 is equal to −1-1.\newline−i2=−(−1)=1-i^2 = -(-1) = 1
  4. Combine like terms: Combine like terms.\newline−9+(−3i)+(−3i)+1=−9+1−3i−3i-9 + (-3i) + (-3i) + 1 = -9 + 1 - 3i - 3i
  5. Simplify the expression: Simplify the expression by adding/subtracting the real parts and the imaginary parts.\newline−9+1−3i−3i=−8−6i-9 + 1 - 3i - 3i = -8 - 6i

More problems from Multiply numbers written in scientific notation

Question
Factor 16a+72 16 a+72 to identify the equivalent expressions.\newlineChoose 22 answers:\newlineA 4(4a+18) 4(4 a+18) \newlineB 8(2a+9) 8(2 a+9) \newlineC 2(8+36a) 2(8+36 a) \newlineD 2(8a+72) 2(8 a+72)
Get tutor helpright-arrow

Posted 10 months ago

Question
Factor 30−6v−18w 30-6 v-18 w to identify the equivalent expressions.\newlineChoose 22 answers:\newlineA 2(15−12v) 2(15-12 v) \newlineB 3(10−3v+6w) 3(10-3 v+6 w) \newlinec 6(5−v−3w) 6(5-v-3 w) \newlineD 2(15−3v−9w) 2(15-3 v-9 w)
Get tutor helpright-arrow

Posted 10 months ago

Question
Factor 24m−12p+72 24 m-12 p+72 to identify the equivalent expressions.\newlineChoose 22 answers:\newlineA 6(4m+2p+12) 6(4 m+2 p+12) \newlineB 2(12m−6p+36) 2(12 m-6 p+36) \newlinec 12(2m−p+6) 12(2 m-p+6) \newlineD 24(m−12p+3) 24(m-12 p+3)
Get tutor helpright-arrow

Posted 10 months ago

Question
Factor 48−8x 48-8 x to identify the equivalent expressions.\newlineChoose 22 answers:\newlineA 3(16−8x) 3(16-8 x) \newlineB 2(24−4x) 2(24-4 x) \newlinec 8(6−x) 8(6-x) \newlineD 4(12−4x) 4(12-4 x)
Get tutor helpright-arrow

Posted 7 months ago

Question
Multiply and simplify the following complex numbers:\newline(−3−2i)⋅(−4+2i) (-3-2 i) \cdot(-4+2 i)
Get tutor helpright-arrow

Posted 10 months ago

Question
Multiply and simplify the following complex numbers:\newline(1−2i)⋅(4+i) (1-2 i) \cdot(4+i)
Get tutor helpright-arrow

Posted 9 months ago

Question
Multiply and simplify the following complex numbers:\newline(−1+4i)⋅(4−3i) (-1+4 i) \cdot(4-3 i)
Get tutor helpright-arrow

Posted 10 months ago

Question
Multiply and simplify the following complex numbers:\newline(−4−4i)⋅(−5−3i) (-4-4 i) \cdot(-5-3 i)
Get tutor helpright-arrow

Posted 10 months ago

Question
Multiply and simplify the following complex numbers:\newline(1+5i)⋅(−3−i) (1+5 i) \cdot(-3-i)
Get tutor helpright-arrow

Posted 10 months ago

Question
Multiply and simplify the following complex numbers:\newline(−2+2i)⋅(5+5i) (-2+2 i) \cdot(5+5 i)
Get tutor helpright-arrow

Posted 10 months ago

View all (25)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant