Powers of i and Conjugates

Authored by Ryan Greene

Mathematics

10th - 12th Grade

CCSS covered

Used 6+ times

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10 questions

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MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Simplify:
i⁷

-i

-1

Tags

CCSS.HSN.CN.A.2

CCSS.HSN.CN.A.1

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Multiply $4-3i$ by its conjugate.

16-9i

16+9i

Tags

CCSS.HSN.CN.A.2

CCSS.HSN.CN.A.3

MULTIPLE SELECT QUESTION

5 mins • 1 pt

Which expression yield a real solution. Select all that apply.

$\left(6i\right)^{27}$

$\left(-9i\right)^{102}$

$17i^8$

$\left(7-8i\right)^2$

$\left(4+5i\right)\left(4-5i\right)$

Tags

CCSS.HSN.CN.A.2

CCSS.HSN.CN.A.1

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

$\left(8+3i\right)\left(8-3i\right)$

Real or Imaginary?

Real

Imaginary

Cannot determine

Tags

CCSS.HSN.CN.A.2

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

$\left(7+4i\right)^2$

Real or Imaginary?

Real

Imaginary

Cannot be determined

Tags

CCSS.HSN.CN.A.2

CCSS.HSN.CN.A.1

MULTIPLE SELECT QUESTION

5 mins • 1 pt

Which statements are true? Select all that apply.

$\sqrt{-4}=-2$

$\sqrt{-4}=2i$

$\sqrt{4i}=2i$

$2\left(i^2\right)^2=2$

$2i^3=-2i$

Tags

CCSS.HSN.CN.A.2

CCSS.HSN.CN.A.1

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

$\left(-5i\right)^{18}$

Real or Imaginary?

Real

Imaginary

Cannot be determined

Tags

CCSS.HSN.CN.A.2

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

$\left(3i\right)^{19}$

Real or Imaginary?

Real

Imaginary

Cannot be determined

Tags

CCSS.HSN.CN.A.2

CCSS.HSN.CN.A.1

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Simplify: $i^{15}$

$i$

$1$

$-i$

$-1$

Tags

CCSS.HSN.CN.A.2

CCSS.HSN.CN.A.1

10.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Simplify: $i^{50}$

$i$

$1$

$-i$

$-1$

Tags

CCSS.HSN.CN.A.2

CCSS.HSN.CN.A.1

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Powers of i and Conjugates

Simplify:i7

Multiply 4−3i4-3i4−3i by its conjugate.

Which expression yield a real solution. Select all that apply.

(8+3i)(8−3i)\left(8+3i\right)\left(8-3i\right)(8+3i)(8−3i) Real or Imaginary?

(7+4i)2\left(7+4i\right)^2(7+4i)2 Real or Imaginary?

Which statements are true? Select all that apply.

(−5i)18\left(-5i\right)^{18}(−5i)18 Real or Imaginary?

(3i)19\left(3i\right)^{19}(3i)19 Real or Imaginary?

Simplify: i15i^{15}i15

Simplify: i50i^{50}i50

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Simplify:
i⁷

Multiply $4-3i$ by its conjugate.

$\left(8+3i\right)\left(8-3i\right)$

Real or Imaginary?

$\left(7+4i\right)^2$

Real or Imaginary?

$\left(-5i\right)^{18}$

Real or Imaginary?

$\left(3i\right)^{19}$

Real or Imaginary?

Simplify: $i^{15}$

Simplify: $i^{50}$