Exercises: Know the Imaginary Unit and Complex Number Form

Show your work where indicated. Write all complex numbers in standard form $a + bi$.

Grade 9·20 problems·~25 min·Common Core Math - HS Number and Quantity·standard·hsn-cn-a-1

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Warm-Up: Review What You Know

Which equation has no solution in the real number system?

$x^2 = 4$

$x^2 = -1$

$x + 3 = 0$

$x^2 = 2$

Which of the following is the correct value of $i^2$ ?

$1$

$i$

$-i$

$-1$

Every real number is also a complex number. Which of the following correctly explains why?

Because complex numbers are always written with a plus sign.

Because any real number $a$ can be written as $a + 0i$ , fitting the $a + bi$ form.

Because complex numbers and real numbers are two names for the same thing.

Because real numbers are larger than complex numbers.

What is the imaginary part of the complex number $-5 + 3i$ ?

$-5$

$3i$

$3$

$5$

Write the real part of $\sqrt{2} - 7i$ . Enter the exact value.

What is the imaginary part of the real number $4$ ? (Rewrite as $4 + {?}i$ .) Enter a number.

Which of the following is a pure imaginary number?

$3 + 2i$

$-7$

$5i$

$0$

Evaluate $i^3$ .

$1$

$-1$

$i$

$-i$

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