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: (-3-2i)*(-4+2i)

Multiply and simplify the following complex numbers:\newline(−3−2i)⋅(−4+2i) (-3-2 i) \cdot(-4+2 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(−3−2i)⋅(−4+2i) (-3-2 i) \cdot(-4+2 i)
  1. Distribute terms in complex numbers: Distribute each term in the first complex number by each term in the second complex number.\newline(−3−2i)(−4+2i)=(−3)(−4)+(−3)(2i)+(−2i)(−4)+(−2i)(2i)(-3-2i)(-4+2i) = (-3)(-4) + (-3)(2i) + (-2i)(-4) + (-2i)(2i)
  2. Multiply real and imaginary parts: Multiply the real parts and the imaginary parts separately.\newline(−3)⋅(−4)=12(-3)\cdot(-4) = 12 (Real part)\newline(−3)⋅(2i)=−6i(-3)\cdot(2i) = -6i (Imaginary part)\newline(−2i)⋅(−4)=8i(-2i)\cdot(-4) = 8i (Imaginary part)\newline(−2i)⋅(2i)=−4i2(-2i)\cdot(2i) = -4i^2 (Real part, because i2=−1i^2 = -1)
  3. Combine like terms: Combine like terms (real with real and imaginary with imaginary).\newlineReal parts: 12+(−4i2)=12−4(−1)=12+4=1612 + (-4i^2) = 12 - 4(-1) = 12 + 4 = 16\newlineImaginary parts: −6i+8i=2i-6i + 8i = 2i
  4. Write final answer as a complex number: Write the final answer as a complex number (a+bi)(a + bi).\newlineFinal answer: 16+2i16 + 2i

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(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

Question
You pick a card at random, put it back, and then pick another card at random.\newline44\newline55\newline66\newline77\newlineWhat is the probability of picking a number greater than 55 and then picking a 44 ?\newlineWrite your answer as a percentage.
Get tutor helpright-arrow

Posted 1 month ago

View all (25)

Related topics

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