Operations with Complex Numbers - Algebra 2
Card 1 of 30
What is $(1-2i)(-4+3i)$ in standard form?
What is $(1-2i)(-4+3i)$ in standard form?
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$2+11i$. Use FOIL: $(1)(-4) + (1)(3i) + (-2i)(-4) + (-2i)(3i) = -4 + 3i + 8i + 6$.
$2+11i$. Use FOIL: $(1)(-4) + (1)(3i) + (-2i)(-4) + (-2i)(3i) = -4 + 3i + 8i + 6$.
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What is $(10-3i)-(4+9i)$ in standard form?
What is $(10-3i)-(4+9i)$ in standard form?
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$6-12i$. Subtract real parts: $10-4=6$, imaginary parts: $-3-9=-12$.
$6-12i$. Subtract real parts: $10-4=6$, imaginary parts: $-3-9=-12$.
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What is $(bi)(di)$ simplified using $i^2=-1$?
What is $(bi)(di)$ simplified using $i^2=-1$?
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$-bd$. Since $(bi)(di) = bdi^2 = bd(-1) = -bd$.
$-bd$. Since $(bi)(di) = bdi^2 = bd(-1) = -bd$.
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What is the value of $i^3$ written in simplest form?
What is the value of $i^3$ written in simplest form?
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$-i$. Since $i^3 = i^2 \cdot i = (-1) \cdot i = -i$.
$-i$. Since $i^3 = i^2 \cdot i = (-1) \cdot i = -i$.
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What is the additive identity for complex numbers?
What is the additive identity for complex numbers?
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$0+0i$. Adding this to any complex number yields the same number.
$0+0i$. Adding this to any complex number yields the same number.
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What is the difference $(a+bi)-(c+di)$ in standard form?
What is the difference $(a+bi)-(c+di)$ in standard form?
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$(a-c)+(b-d)i$. Subtract real parts and imaginary parts separately.
$(a-c)+(b-d)i$. Subtract real parts and imaginary parts separately.
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What is $(3+2i)+(5-7i)$ in standard form?
What is $(3+2i)+(5-7i)$ in standard form?
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$8-5i$. Add real parts: $3+5=8$, imaginary parts: $2+(-7)=-5$.
$8-5i$. Add real parts: $3+5=8$, imaginary parts: $2+(-7)=-5$.
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What is the product $(a+bi)(c+di)$ in standard form?
What is the product $(a+bi)(c+di)$ in standard form?
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$(ac-bd)+(ad+bc)i$. Use FOIL and $i^2 = -1$ to simplify.
$(ac-bd)+(ad+bc)i$. Use FOIL and $i^2 = -1$ to simplify.
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What is the value of $i^2$?
What is the value of $i^2$?
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$-1$. By definition of the imaginary unit.
$-1$. By definition of the imaginary unit.
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What is $(a+bi)+(c-di)$ simplified in standard form?
What is $(a+bi)+(c-di)$ simplified in standard form?
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$(a+c)+(b-d)i$. Add real parts and subtract imaginary parts.
$(a+c)+(b-d)i$. Add real parts and subtract imaginary parts.
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What is $(a+bi)-(c-di)$ simplified in standard form?
What is $(a+bi)-(c-di)$ simplified in standard form?
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$(a-c)+(b+d)i$. Distribute the negative sign to both terms inside parentheses.
$(a-c)+(b+d)i$. Distribute the negative sign to both terms inside parentheses.
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What is $(a+bi)(a-bi)$ simplified using $i^2=-1$?
What is $(a+bi)(a-bi)$ simplified using $i^2=-1$?
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$a^2+b^2$. Conjugate multiplication yields sum of squares.
$a^2+b^2$. Conjugate multiplication yields sum of squares.
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What is $(4+3i)(4-3i)$ in standard form?
What is $(4+3i)(4-3i)$ in standard form?
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$25$. Difference of squares: $(4)^2 - (3i)^2 = 16 - 9i^2 = 16 + 9 = 25$.
$25$. Difference of squares: $(4)^2 - (3i)^2 = 16 - 9i^2 = 16 + 9 = 25$.
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What is $(3-2i)(-1+i)$ in standard form?
What is $(3-2i)(-1+i)$ in standard form?
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$-1+5i$. Use FOIL: $(3)(-1) + (3)(i) + (-2i)(-1) + (-2i)(i) = -3 + 3i + 2i + 2$.
$-1+5i$. Use FOIL: $(3)(-1) + (3)(i) + (-2i)(-1) + (-2i)(i) = -3 + 3i + 2i + 2$.
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What is the value of $i^5$ written in simplest form?
What is the value of $i^5$ written in simplest form?
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$i$. Since $i^5 = i^4 \cdot i = 1 \cdot i = i$.
$i$. Since $i^5 = i^4 \cdot i = 1 \cdot i = i$.
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What is $(7i)(-3i)$ simplified?
What is $(7i)(-3i)$ simplified?
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$21$. Since $(7i)(-3i) = -21i^2 = -21(-1) = 21$.
$21$. Since $(7i)(-3i) = -21i^2 = -21(-1) = 21$.
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What is the sum $(a+bi)+(c+di)$ in standard form?
What is the sum $(a+bi)+(c+di)$ in standard form?
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$(a+c)+(b+d)i$. Add real parts and imaginary parts separately.
$(a+c)+(b+d)i$. Add real parts and imaginary parts separately.
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What is the value of $i^2$?
What is the value of $i^2$?
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$-1$. By definition of the imaginary unit.
$-1$. By definition of the imaginary unit.
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What is $(a+bi)(a-bi)$ simplified using $i^2=-1$?
What is $(a+bi)(a-bi)$ simplified using $i^2=-1$?
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$a^2+b^2$. Conjugate multiplication yields sum of squares.
$a^2+b^2$. Conjugate multiplication yields sum of squares.
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What is $(-3+4i)-(8+i)$ in standard form?
What is $(-3+4i)-(8+i)$ in standard form?
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$-11+3i$. Subtract real parts: $-3-8=-11$, imaginary parts: $4-1=3$.
$-11+3i$. Subtract real parts: $-3-8=-11$, imaginary parts: $4-1=3$.
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What is the real part of the complex number $a+bi$?
What is the real part of the complex number $a+bi$?
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$a$. The coefficient of the non-imaginary term.
$a$. The coefficient of the non-imaginary term.
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What is $(1+i)(1+i)$ in standard form?
What is $(1+i)(1+i)$ in standard form?
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$2i$. Use FOIL: $(1)(1) + (1)(i) + (i)(1) + (i)(i) = 1 + i + i - 1 = 2i$.
$2i$. Use FOIL: $(1)(1) + (1)(i) + (i)(1) + (i)(i) = 1 + i + i - 1 = 2i$.
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What is the value of $i^6$ written in simplest form?
What is the value of $i^6$ written in simplest form?
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$-1$. Since $i^6 = (i^2)^3 = (-1)^3 = -1$.
$-1$. Since $i^6 = (i^2)^3 = (-1)^3 = -1$.
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What is $(5-2i)(1+3i)$ in standard form?
What is $(5-2i)(1+3i)$ in standard form?
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$11+13i$. Use FOIL: $(5)(1) + (5)(3i) + (-2i)(1) + (-2i)(3i) = 5 + 15i - 2i + 6$.
$11+13i$. Use FOIL: $(5)(1) + (5)(3i) + (-2i)(1) + (-2i)(3i) = 5 + 15i - 2i + 6$.
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What is $(2+5i)(-3-2i)$ in standard form?
What is $(2+5i)(-3-2i)$ in standard form?
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$4-19i$. Use FOIL: $(2)(-3) + (2)(-2i) + (5i)(-3) + (5i)(-2i) = -6 - 4i - 15i - 10$.
$4-19i$. Use FOIL: $(2)(-3) + (2)(-2i) + (5i)(-3) + (5i)(-2i) = -6 - 4i - 15i - 10$.
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What is $(8+0i)-(3+0i)$ in standard form?
What is $(8+0i)-(3+0i)$ in standard form?
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$5$. Subtract real parts only: $8-3=5$, imaginary parts are zero.
$5$. Subtract real parts only: $8-3=5$, imaginary parts are zero.
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What is $(-5i)+(12i)$ in standard form?
What is $(-5i)+(12i)$ in standard form?
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$7i$. Add imaginary parts: $-5i + 12i = 7i$.
$7i$. Add imaginary parts: $-5i + 12i = 7i$.
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What is $(1-i)(1-i)$ in standard form?
What is $(1-i)(1-i)$ in standard form?
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$-2i$. Use FOIL: $(1)(1) + (1)(-i) + (-i)(1) + (-i)(-i) = 1 - i - i - 1 = -2i$.
$-2i$. Use FOIL: $(1)(1) + (1)(-i) + (-i)(1) + (-i)(-i) = 1 - i - i - 1 = -2i$.
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What is $(1+i)(1-i)$ in standard form?
What is $(1+i)(1-i)$ in standard form?
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$2$. Difference of squares: $(1)^2 - (i)^2 = 1 - i^2 = 1 + 1 = 2$.
$2$. Difference of squares: $(1)^2 - (i)^2 = 1 - i^2 = 1 + 1 = 2$.
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What is $(2- i)(-5- i)$ in standard form?
What is $(2- i)(-5- i)$ in standard form?
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$-11+3i$. Use FOIL: $(2)(-5) + (2)(-i) + (-i)(-5) + (-i)(-i) = -10 - 2i + 5i - 1$.
$-11+3i$. Use FOIL: $(2)(-5) + (2)(-i) + (-i)(-5) + (-i)(-i) = -10 - 2i + 5i - 1$.
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