Complex numbers - polar form

When a complex number is drawn on the complex plane. The distance from the origin is the value of

• the argument

• The modulus

• The real co-efficient

• The imaginary co-efficient

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CCSS.HSN.CN.A.3

CCSS.HSN.CN.B.5

CCSS.HSN.CN.B.6

The argument measures the angle

• clockwise from the y-axis

• anti clockwise from the y-axis

• anti clockwise from the x-axis

• clockwise from the x-axis

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CCSS.HSF.TF.A.2

 for an imaginary number z=a+bi, the modulus squared  $\left|z\right|^2$  is given by

•  $\sqrt{a^2+b^2}$  

•  $\tan^{-1}\left(\frac{b}{a}\right)$  

•  $\tan\left(\frac{a}{b}\right)$  

•  $a^2+b^2$  

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CCSS.HSN.CN.B.6

For the number -1+5i the argument measured in degrees would be

• between 0 and 90°

• between 0 and -90°

• between 90° and 180°

• between -90° and -180°

Tags

CCSS.HSN.CN.B.4

For the number 2-3i the argument measured in degrees would be

• between 0 and 90°

• between 0 and -90°

• between 90° and 180°

• between -90° and -180°

Tags

CCSS.HSN.CN.B.4

CCSS.HSN.CN.B.5

For the number -7-8i the argument measured in degrees would be

• between 0 and 90°

• between 0 and -90°

• between 90° and 180°

• between -90° and -180°

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CCSS.HSN.CN.B.4

CCSS.HSN.CN.B.5

For the number 3+4i the argument measured in degrees would be

• between 0 and 90°

• between 0 and -90°

• between 90° and 180°

• between -90° and -180°

Tags

CCSS.HSN.CN.B.4

CCSS.HSN.CN.B.5

i⁴²=

• i

• -i

• -1

• 1

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CCSS.HSN.CN.A.1

6i(a+bi)= 42+ 60i

Therefore a=

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CCSS.HSN.CN.A.2

(4+6i)(a+5i)= -18+ 38i

Therefore a=

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CCSS.HSN.CN.A.2