How to subtract complex numbers

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ACT Math › How to subtract complex numbers

Questions 1 - 5

Complex numbers take the form , where is the real term in the complex number and is the nonreal (imaginary) term in the complex number.

Which of the following isincorrect?

Explanation

A problem like this can be solved similarly to a linear binomial like /

Subtract from , given:

Explanation

A complex number is a combination of a real and imaginary number. To subtract complex numbers, subtract each element separately.

In equation , is the real component and is the imaginary component (designated by ). In equation , is the real component and is the imaginary component. Solving for ,

$b-a = \left ( 4-2i\right ) - \left ( 3 + i\right ) = \left ( 4-3\right ) + i\left ( -2-1\right ) = 1 - 3i$

Complex numbers take the form , where is the real term in the complex number and is the nonreal (imaginary) term in the complex number.

Simplify:

$\textup{None of these}$

Explanation

Solving this equation is very similar to solving a linear binomial like . To solve, just combine like terms, being careful to watch for double negatives.

Complex numbers take the form , where is the real term in the complex number and is the nonreal (imaginary) term in the complex number.

Which of the following equations simplifies into ?

Explanation

This equation can be solved very similarly to a binomial like .

Simplify the exponent,

$(3^{6})^{2}$ .

$3^{12}$

$3^{4}$

$3^{8}$

$3^{3}$

Explanation

When you have an exponent on the outside of parentheses while another is on the inside of the parentheses, such as in $(3^{6})^{2}$ , multiply the exponents together to get the answer: $3^{12}$ .

This is different than when you have two numbers with the same base multiplied together, such as in $x^{2} \cdot x^{3} = x^{5}$ . In that case, you add the exponents together.

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