Q&A for How to Simplify Complex Numbers

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What if there's only 1 number for the denominator when it comes to complex numbers? For example: 8 - 3i/-2i? What would the conjugate be for the denominator?

Technist

Community Answer

Here, your denominator has a real number of 0 and a complex number of -2. So what you're really seeing is (8-3i)/(0-2i). So the conjugate would be 0+2i, or simply 2i. You multiply with that and it cancels out the 'i' in the denominator.

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Question

How do you simplify an expression like 8(i^60)?

Alphabet

Community Answer

It is known that i^1 = i = sqrt(-1), i^2 = -1, i^3 = -i, and i^4 = 1. Therefore we can split up large exponents like so: 8i^60 = 8 * (i^4)^15 = 8 * (1)^15 = 8.

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How to simplify if you have -6i³+i²?

Orlando Huang

Community Answer

You can't sumplify, you can only solve. -6*-i=6i, i^2=-1. 6i+-1=-1+6i. ∴-6i^3+i^2=-1+6i.

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Question

How can you simply question like: (-3 + 4i + 2i*8)( 1/2 - 6*9)?

Bella Johnston

Community Answer

When simplifying an equation like this, you need to combine like terms. Like terms are numbers that have the same coefficient (in this case, the letter "i"). So, first should combine like terms (everything with the letter "i"). Therefore, combine 4i + 2i. Now the equation is (-3 + 6i * 8)(1/2 - 6 * 9). Now solve like terms in each set of parenthesis. So the equation is (-24 + 6i)(54.5). Now drop the parentheses (because there are no more like terms in them) and solve! -24 + 6i * 54.5 = 6i * 54.5 - 24 = 6i - 30.5.

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Can 28-4i be simplified?

Donagan

Top Answerer

Not really. You can do this: 4(7 - i), but that's all.

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If a= -x and b= (-2 + 4i), what is the value of ab^2?

Community Answer

ab² = (-x)(-2 + 4i)² = (-x)(-2 + 4i)(-2 + 4i) = (-x)(4 -16i + 16i²) = (-x)(4 -16i -16) = (-x)(-12 -16i) = 12x + 16i x.

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Solve -5+5i divided by -2-9i

I_l1ke_gam3s

Community Answer

-5+5i/-2 - 9i. Multiply by the conjugate of the denominator, aka -2 + 9i. Multiply that on the numerator and denominator (-5 + 5i)(-2 + 9i) = 10 - 45i - 10i + 45i^2. 10 - 55i + 45(-1) = 10 - 55i - 45 = -35 - 55i. For the denominator, (-2 - 9i)(-2 + 9i) = 4 -18i + 18i - 81i^2 = 4 + 81 = 85. (-35 - 55i)/85 = -35/85 - 55/85i = -7/17 - 11/17i.

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